A structure of tunable dual-bandpass microwave photonic filter (MPF) based on chirped fiber Bragg grating (CFBG) is proposed and experimentally demonstrated. By using two cascaded CFBGs with different central reflection wavelengths, bandwidths and chirp parameters, and the different delays of the modulated light signal in this structure are introduced. Consequently, two different frequency passbands are realized. On this basis, by adjusting the variable optical delay line in Mach-Zehnder interferometer (MZI) to change the free spectral range of MPF, the central frequencies of the two passbands can be tuned. Two different passbands with the central frequencies of 6.75 GHz and 16.07 GHz are obtained in the experiment. By adjusting the optical path difference between the two arms of MZI, the tuning of the central frequency of MPF is achieved. The proposed dual-bandpass MPF has a simple structure and is of good tunability and stability.