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A wideband frequency-tunable optoelectronic oscillator (OEO) based on a narrowband phase-shifted fiber Bragg grating (PSFBG) and wavelength tuning of the laser is proposed and demonstrated. With assistance of an optical single-sideband modulator, the PSFBG with a narrow transmission peak acts like an equivalent high-Q microwave filter to select the oscillation frequency. Frequency tunability of the OEO can be simply realized by tuning the wavelength of a laser source. An X-band optoelectronic oscillating signal with frequency tunable at wide range from 8.4 to 11.8 GHz is generated and its performance is investigated in the experiment.