In this paper, we propose a novel approach to implementing an all-optical microwave filter that is suitable for direct deployment in a radio-over-fiber link. The proposed filter consists of a narrow linewidth laser source, two Mach-Zehnder electro-optic intensity modulators (MZM), a local RF signal source and a chirped fiber Bragg grating (CFBG). The light emitted from the laser source is externally intensity modulated by a driving RF signal (RF1), and then injected to a second electro-optic intensity modulator. The second intensity modulator is driven by a strong local RF signal (RF2), to produce a spectrum with a carrier and multiple sidebands. Thanks to the frequency mixing effect of the second intensity modulator, the RF signal carried by the optical source is transferred to the sidebands as well. By using a CFBG as a dispersive device to induce time delays for the carrier and the sidebands, an all-optical microwave filter with only a single light source, but multiple taps is realized. The tunability of the proposed filter can be achieved by adjusting the frequency of RF2. A 2-tap lowpass filter with a free spectral range (FSR) tunable from 2.1 GHz to 4.2 GHz, and a 3-tap lowpass filter with a free spectral range tunable from 4.2 GHz to 4.8 GHz are experimentally demonstrated.