UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

SCHEDULE 13D

(Amendment No.    )*

Under the Securities Exchange Act of 1934

TW TELECOM INC.

(Name of Issuer)

Common Stock, par value $0.01 per share

(Title of Class of Securities)

87311L104

(CUSIP Number)

Keith Meister

Corvex Management LP

712 Fifth Avenue, 23rd Floor

New York, New York 10019

(212) 474-6700

(Name, Address and Telephone Number of Person Authorized to Receive Notices and Communications)

COPIES TO:

Patrick J. Dooley, Esq.

Akin Gump Strauss Hauer & Feld LLP

One Bryant Park

New York, NY 10036

(212) 872-1000

May 8, 2013

(Date of Event which Requires Filing of this Statement)

If the filing person has previously filed a statement on Schedule 13G to report the acquisition that is the subject of this Schedule 13D, and is filing this schedule because of §§240.13d-1(e), 240.13d-1(f) or 240.13d-1(g), check the following box  ¨.

Note: Schedules filed in paper format shall include a signed original and five copies of the schedule, including all exhibits. See Rule §240.13d-7 for other parties to whom copies are to be sent.

The information required on the remainder of this cover page shall not be deemed to be “filed” for the purpose of Section 18 of the Securities Exchange Act of 1934 (“Act”) or otherwise subject to the liabilities of that section of the Act but shall be subject to all other provisions of the Act (however, see the Notes).

Continued on following page(s)

The title of the class of equity security to which this statement on Schedule 13D relates is the Common Stock, par value $0.01 per share (the “Shares”) of tw telecom inc., a Delaware corporation (the “Issuer”). The address of the Issuer’s principal executive offices is 10475 Park Meadows Drive, Littleton, Colorado 80124.

This statement on Schedule 13D is filed on behalf of Corvex Management LP, a Delaware limited partnership (“Corvex”), and Keith Meister, a U.S. citizen (collectively, the “Reporting Persons”). This statement relates to Shares held for the account of certain private investment funds for which Corvex acts as investment adviser, including Corvex Master Fund, LP, a Cayman Islands limited partnership, the general partner of which is controlled by Mr. Meister (collectively, the “Corvex Funds”). The general partner of Corvex is controlled by Mr. Meister. The principal business address of each of Corvex and Mr. Meister is 712 Fifth Avenue, 23 Floor, New York, NY 10019. A joint filing agreement of Corvex and Mr. Meister is attached hereto as Exhibit 1.

During the last five years, none of Corvex, Mr. Meister or any of the Corvex Funds has been convicted in a criminal proceeding (excluding traffic violations or similar misdemeanors) or has been a party to a civil proceeding of a judicial or administrative body of competent jurisdiction and as a result of such proceeding was or is subject to a judgment, decree or final order enjoining future violations of, or prohibiting or mandating activities subject to, federal or state securities laws or finding any violation with respect to such laws.

The responses to Items 4, 5 and 6 of this Schedule 13D are incorporated herein by reference.

The Reporting Persons used working capital of the Corvex Funds to purchase the 8,669,424 Shares reported herein and to acquire the call options and put options referenced in Item 6. The total purchase price for the Shares reported herein was $58,253,245 and the purchase price to acquire such call options and put options was $52,486,104.

The Reporting Persons may effect purchases of securities through margin accounts maintained for it with brokers, which extend margin credit as and when required to open or carry positions in their margin accounts, subject to applicable federal margin regulations, stock exchange rules and such firms’ credit policies. Positions in Shares may be held in margin accounts and may be pledged as collateral security for the repayment of debit balances in the accounts.

The responses to Items 3, 5 and 6 of this Schedule 13D are incorporated herein by reference.

The Reporting Persons acquired the Shares over which they exercise beneficial ownership in the belief that the Shares are undervalued and are an attractive investment. Certain of the Reporting Persons have had multiple conversations and meetings with the management of the Issuer to discuss the Issuer’s business and strategies and will seek to have additional conversations with one or more of management, the board, other stockholders of the Issuer and other persons to discuss the Issuer’s business, strategies and other matters related to the Issuer. These discussions have reviewed, and may continue to review, options for enhancing shareholder value through various strategic alternatives including, but not limited to, improving capital structure and/or capital allocation through increased leverage and stock repurchases or dividends, among other actions, M&A, and general corporate strategies.

The Reporting Persons intend to review their respective investment in the Issuer on a continuing basis and may from time to time and at any time in the future depending on various factors, including, without limitation, the outcome of any discussions referenced above, the Issuer’s financial position and strategic direction, actions taken by the board, price levels of the Shares, other investment opportunities available to the Reporting Persons, conditions in the securities market and general economic and industry conditions, take such actions with respect to the investment in the Issuer as they deem appropriate, including: (i) acquiring additional Shares and/or other equity, debt, notes, other securities, or derivative or other instruments that are based upon or relate to the value of the Shares or the Issuer (collectively, “Securities”) of the Issuer in the open market or otherwise; (ii) disposing of any or all of their Securities in the open market or otherwise; (iii) engaging in any hedging or similar transactions with respect to the Securities; or (iv) proposing or considering one or more of the actions described in subsections (a) through (j) of Item 4 of Schedule 13D.

(a) – (b) Corvex may be deemed to be the beneficial owner of 2,294,924 Shares and 6,374,500 Shares underlying the call options referenced in Item 6, which collectively represent approximately 5.77% of the Issuer’s outstanding Shares. Corvex may be deemed to have sole power to vote and sole power to dispose of 8,669,424 Shares. By virtue of his position as control person of the general partner of Corvex, Mr. Meister may be considered to beneficially own such Shares.

The percentage calculated in the immediately foregoing paragraph is calculated based on a total of 150,321,589 Shares outstanding as of April 30, 2013 (based on the Issuer’s Quarterly Report on Form 10-Q for the period ending March 31, 2013).

(c) Except as set forth on Exhibit 2 attached hereto, there have been no transactions with respect to the Shares during the sixty days prior to the date hereof by any of the Reporting Persons.

(d) The limited partners of (or investors in) each of the private investment funds, or their respective subsidiaries or affiliated entities, for which Corvex or its affiliates acts as general partner and/or investment adviser have the right to participate in the receipt of dividends from, or proceeds from the sale of, the Shares held for the accounts of their respective funds in accordance with their respective limited partnership interests (or investment percentages) in their respective funds.

(e) Not applicable.

The responses to Items 3, 4 and 5 of this Schedule 13D are incorporated herein by reference.

Corvex purchased in the over the counter market American-style call options referencing an aggregate of 6,374,500 Shares, which have an exercise price of $18.00 per Share and expire on February 28, 2014.

Corvex sold in the over the counter market European-style put options referencing an aggregate of 6,374,500 Shares at an exercise price of $18.00 per Share, which expire on the earlier of February 28, 2014 or the date on which the corresponding American-style call option described above in this Item 6 is exercised.

Except for the arrangements described herein, to the best knowledge of the Reporting Persons, there are no contracts, arrangements, understandings or relationships (legal or otherwise) among the persons named in Item 2 and between such persons and any other person with respect to any securities of the Issuer, including but not limited to, transfer or voting of any of the securities, finder’s fees, joint ventures, loan or option arrangements, puts or calls, guarantees of profits, division of profits or loss, or the giving or withholding of proxies.

Exhibit 1—Agreement by and among Corvex and Keith Meister to file this Schedule 13D and any amendments thereto jointly on behalf of each of them.

Exhibit 2—Transactions in the Shares effected in the past 60 days.

SIGNATURES

After reasonable inquiry and to the best of my knowledge and belief, the undersigned certifies that the information set forth in this statement is true, complete and correct.

EXHIBIT 1

AGREEMENT

JOINT FILING OF SCHEDULE 13D

The undersigned hereby agree to jointly prepare and file with regulatory authorities this Schedule 13D and any future amendments thereto reporting each of the undersigned’s ownership of securities of tw telecom inc., and hereby affirm that such Schedule 13D is being filed on behalf of each of the undersigned pursuant to and in accordance with the provisions of Rule 13d-1(k) under the Securities Exchange Act of 1934. The undersigned acknowledge that each shall be responsible for the timely filing of such amendments, and for the completeness and accuracy of the information concerning him or it contained therein, but shall not be responsible for the completeness and accuracy of the information concerning the other, except to the extent that he or it knows or has reason to believe that such information is inaccurate.

EXHIBIT 2

TRANSACTIONS

The following table sets forth all transactions with respect to Shares effected in the last sixty days by the Reporting Persons on behalf of the Reporting Persons in respect of the Shares, inclusive of any transactions effected through 4:00 p.m., New York City time, on May 8, 2013. Except as otherwise noted below, all such transactions were purchases or sales of Shares effected in the open market, and the table includes commissions paid in per share prices.