A tunable mode convertor is experimentally demonstrated based on a fiber Bragg grating (FBG), which is fabricated in a graded-index nine-mode fiber by using a femtosecond laser. Nine linearly polarized (LP) modes were excited and the coupling efficiency of them can reach 90%. By adjusting the polarization controller, the ±1st-, ±2nd-, ±3rd-, and ±4th-order orbital angular momentum (OAM) modes were excited, which means the OAM tuning of 0-±1ℏ, 0-±2ℏ, 0-±3ℏ, and 0-±4ℏ were achieved. LP21/LP02, LP31/LP12, LP41/LP22/LP03 modes were successfully tuned at 1556.00 nm, 1555.10 nm, and 1554.25 nm by twisting the FBG, respectively. Moreover, combined with polarization and torsion control, the tuning between 0th- and -2nd-order OAM has been realized, which is converted from the tuning between LP02 and LP21. By using this method, the OAM tuning of ±1-±3ℏ and ±4-0-±2ℏ may be further realized theoretically.