In this paper, using a fully digital programmable optical frequency comb, a new kind of programmable microwave photonic filter based on stimulated Brillouin scattering is proposed. The principle and experiments scheme are described according to the filtering model established. In experiments, a reconfigurable microwave photonic filter is achieved, showing a tunable range of 0.1~1 GHz, flat top of passband responses and tunable central frequency in a large range of 4~24 GHz. Compared with the microwave photonic filters based on analog signal control, this microwave photonic filter scheme is fully digitally controlled and programmable.