A novel realization of a tunable optoelectronic oscillator (OEO) based on a dual-parallel Mach-Zehnder modulator (DPMZM) and two tunable microwave phase shifters (PS) is experimentally demonstrated. By adjusting the time delay of the microwave signal which is sent to two radio frequency (RF) ports of DPMZM, the center frequency of the multiband microwave photonics filter (MMPF) can be tuned. When the OEO feedback loop is closed, single-frequency microwave signals with a tuning range from 3.6 to 15.6 GHz are generated. The side mode suppression ratio is 67 dB, and the phase noise is measured to be - 104 dBc/Hz when the oscillation frequency is 9.2 GHz. The frequency drift is less than 24 kHz in 1600 s without phase-locked or compensation devices.