A tunable optoelectronic oscillator (OEO) implemented by using a carrier phase-shifted double sideband modulation (CPS-DSB) system consisting of an optical coupler (OC), a Mach–Zehnder modulator (MZM) biased at the minimum transmission point, a polarization beam splitter (PBS), and a tunable optical delay line (TODL) is proposed and experimentally demonstrated. The key device in the system is the CPS-DSB system, which functions in conjunction with a chirped fiber Bragg grating (CFBG) in the loop form a high-Q microwave photonic filter (MPF). Through simply adjusting the TODL, the central frequency of the MPF is shifted and the frequency tunability of the OEO can be realized. A detailed theoretical analysis is provided and the results are confirmed by an experiment. A microwave signal with a frequency-tuning range from 7.24 to 14.05GHz is generated. The phase noise, the long-term stability and the side-mode suppression performance of the generated microwave signal are also investigated.