We demonstrate operation of a tunable mode-locked thulium-doped fiber laser, based on a wavelength-selective chirped fiber Bragg grating (CFBG). By applying strain to the CFBG, we shift its reflection band and can thereby tune the emission-wavelength of the fiber laser between 2022nm and 2042 nm. We obtain a pulse train at 9.4MHz repetition rate and a pulse duration between 9.0 and 12.8 ps. To the best of our knowledge, we report the first tunable mode-locked thulium-doped fiber laser using a tunable CFBG as wavelength-selective element.