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A novel approach to the generation of an optical frequency comb with a widely tunable center wavelength and comb spacing based on an optoelectronic oscillator (OEO) is proposed and experimentally demonstrated. The OEO is implemented using a polarization modulator (PolM), a phase-shifted fiber Bragg grating (PS-FBG), and a photodetector (PD). The PolM is a special phase modulator that supports phase modulation along the two principal axes with opposite modulation indexes. The joint operation of the PolM, the PS-FBG, and the PD corresponds to a frequency-tunable microwave photonic bandpass filter. When the output from the PD is fed back to the PolM, the OEO starts to oscillate and the oscillation frequency can be tuned by tuning the center frequency of the microwave photonic bandpass filter through tuning the optical wavelength. The optical comb is then generated by tapping part of the optical signal from the PolM and sending it to a second PolM. The joint operation of the two PolMs generates an optical comb with the comb spacing tunable by tuning the center frequency of the microwave photonic filter. Through introducing a second wavelength into the OEO, a duplicated optical comb at the second wavelength is generated. An experiment is performed. An optical frequency comb with tunable frequency spacing from 6.6 to 15.3 GHz and a tunable center wavelength from 1500 to 1580 nm is generated.