A novel photonics-assisted method for tunable microwave frequency comb (MFC) generation based on an actively mode-locked optoelectronic oscillator (AML-OEO) is proposed and experimentally demonstrated in this letter. Two key factors for the proposed system, periodic gain modulation and widely tunable center frequency, are implemented by an externally introduced intensity-modulated optical signal and a microwave photonic filter (MPF) based on the phase-shifted fiber Bragg grating (PS-FBG) respectively. Unlike a conventional OEO with only one dominant oscillation mode, an AML-OEO operates in a stable multimode oscillation state and thus can generate MFC signal. Through simply adjusting the center frequency of the PS-FBG-based MPF, the center frequency of the generated MFC changes accordingly. In the proof-of-principle experiment, two sets of MFC signals with center frequency tuning from 3.5 GHz to 6.5 GHz and frequency intervals of 1.02 MHz and 340.46 kHz are generated.