A tunable optoelectronic oscillator (OEO), which employs an all-optical microwave photonic filter (MPF) consisting of two laser sources (LD1 and LD2), an optical coupler (OC, 50:50), a Mach-Zehnder modulator (MZM), and a chirped fiber Bragg grating, is proposed. Because the central frequency of the all-optical MPF can be shifted by changing the wavelength spacing between the two laser sources, the frequency tunability of the OEO can be realized by incorporating such an all-optical MPF into an optical domain dual-loop OEO without any electronic microwave filters. A detailed theoretical analysis is presented and the results are confirmed by an experiment. A microwave signal with a frequency-tuning range from 4.057 to 8.595 GHz is generated. The phase noise, the long-term stability, and the side-mode suppression performance of the generated microwave signal are also investigated.