A tunable dual-frequency optoelectronic oscillator (OEO) based on a tunable dual-passband microwave photonic filter (DPMPF) is proposed and demonstrated. The DPMPF is based on phase-to-intensity modulation (PM-IM) conversion and stimulated Brillouin scattering (SBS). Two pump lightwaves are generated through carrier-suppression doublesideband modulation (CS-DSB) in a Mach-Zehnder modulator (MZM) to generate two SBS gain regions in a single mode fiber. Two SBS gain regions act on the phase modulation signal to achieve a dual-passband filter. Through simply varying the frequency of the radio frequency (RF) signal used for CS-DSB, the two central frequencies of the OEO can be tuned with the frequency interval kept constant. In addition, adjusting the frequency of tunable optical source launched to the MZM, the frequency interval of the OEO can be tuned. In the experiment, the dual-frequency OEOs with frequency intervals of 0.2 GHz and 1.2 GHz are achieved, respectively. The frequency tuning range from 3 to 8 GHz is demonstrated. The dual-frequency OEO with the frequency interval tuned is also achieved.