A tunable frequency-multiplying optoelectronic oscillator (OEO) based on a dual-parallel Mach-Zehnder modulator (DPMZM) is proposed and experimentally demonstrated. In the proposed system, the tunable fundamental microware signal is generated by a tunable optoelectronic oscillator incorporating a phase-shifted fiber Bragg grating (PS-FBG). By adjusting the DC bias of the DPMZM, the frequency-doubled microwave signal with a tunable frequency range from 11 GHz to 20 GHz and the frequency-quadrupled microwave signal with a tunable frequency range from 22.5 GHz to 26 GHz are generated. The phase noises of the fundamental, frequency-doubled and frequency- quadrupled signals at 10 kHz offset frequency are -105.9 dBc/Hz, -103.3 dBc/Hz and -86.2 dBc/Hz, respectively.