UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                    FORM 13F

                               FORM 13F COVER PAGE

Report for the Calendar Quarter Ended:  December 31, 2010

Check here if Amendment [ ]; Amendment Number: ______

   This Amendment (Check only one.):   [ ] is a restatement.
                                       [ ] adds new holdings entries.

Institutional Investment Manager Filing this Report:

Name: Group VI 31, LLC
Address: 201 Main Street, Suite 3100, Fort Worth, Texas 76102

Form 13F File Number:

The institutional investment manager filing this report and the person by whom
it is signed hereby represent that the person signing the report is authorized
to submit it, that all information contained herein is true, correct and
complete, and that it is understood that all required items, statements,
schedules, lists, and tables, are considered integral parts of this form.

Person Signing this Report on Behalf of Reporting Manager:

Name:  Kevin G. Levy
Title: Vice President
Phone: 817-390-8400

Signature, Place, and Date of Signing:

     /s/ Kevin G. Levy                Fort Worth, Texas      February 10, 2011
    ------------------------         -------------------    -------------------
           [Signature]                  [City, State]             [Date]

Report Type (Check only one.):

[ ] 13F HOLDINGS REPORT.  (Check here if all holdings of this reporting
    manager are reported in this report.)

[ ] 13F NOTICE.  (Check here if no holdings reported are in this report, and
    all holdings are reported by other reporting manager(s).)

[X] 13F COMBINATION REPORT. (Check here if a portion of the holdings for this
    reporting manager are reported in this report and a portion are reported by
    other reporting manager(s).)


List of Other Managers Reporting for this Manager:

[If there are no entries in this list, omit this section.]

   Form 13F File Number        Name
                               FW Oak Hill Accretive Healthcare Investors, L.P.





                             FORM 13F SUMMARY PAGE

Report Summary:

Number of Other Included Managers: 0

Form 13F Information Table Entry Total: 1

Form 13F Information Table Value Total: $3,095 (thousands)

List of Other Included Managers:

NONE





                           FORM 13F INFORMATION TABLE




       COLUMN 1               COLUMN 2          COLUMN 3   COLUMN 4        COLUMN 5           COLUMN 6   COLUMN 7      COLUMN 8

                                                                      Shares or
                                                  CUSIP     Value     Principal   SH/  Put/ Investment   Other   Voting Authority
Name of Issuer                Title of Class     Number    (X$1000)    Amount     PRN  Call Discretion  Managers Sole   Shared  None
- --------------                --------------     ------    --------    ------     ---  ----  ---------  -------- ----  ------ ----
                           

JAZZ PHARMACEUTICALS INC       COM             472147107      3095      157247    SH          DEFINED            157247