A dual-band bandpass microwave photonic filter (MPF) based on stimulated Brillouin scattering (SBS) is theoretically analyzed and experimentally demonstrated. Two separated tunable laser sources (TLSs) are employed to generate two passbands by implementing phase modulation to amplitude modulation conversion by using SBS induced sideband amplification. The center frequencies of both passbands can be independently tuned ranging from 1 GHz to 19 GHz. High resolution with 3 dB bandwidth less than 30 MHz and large out-of-band rejection about 40 dB under 25 mW optical pump power are achieved.