An optically tunable optoelectronic oscillator (OEO) with a wide frequency tunable range incorporating a tunable microwave photonic filter implemented based on phase-modulation to intensity-modulation conversion using a phase-shifted fiber Bragg grating (PS-FBG) is proposed and experimentally demonstrated. The PS-FBG in conjunction with two optical phase modulators in the OEO loop form a high-Q, wideband and frequency-tunable microwave photonic bandpass filter, to achieve simultaneously single-frequency selection and frequency tuning. Since the tuning of the microwave filter is achieved by tuning the wavelength of the incident light wave, the tunability can be easily realized at a high speed. A theoretical analysis is performed, which is verified by an experiment. A microwave signal with a frequency tunable from 3 GHz to 28 GHz is generated. To the best of our knowledge, this is the widest frequency tunable range ever achieved by an OEO. The phase noise performance of the OEO is also investigated.