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A kinetic model of atmospheric streamer discharges on conductors with surface protrusion is first presented. The formations of streamer discharges in air on both the smooth conductors and rough conductors with different surface protrusions have been studied by using two-dimensional particle-in-cell simulations complemented by Monte Carlo collisions (PIC-MCC). The evolutions of electric fields, plasma densities as well as the propagation velocity of the streamers are demonstrated. Moreover, the influences of the sizes of surface protrusions on development of the discharge have been investigated. It is shown that, compared with the discharge on a smooth conductor, the streamer discharge is greatly favored by the protrusion, whose maximum electric field, electron density and propagation velocity are increased. Under the same discharge conditions, the discharges with medium sizes of the protrusions are the strongest, rather than those with protrusions of small size or big size. Our results reveal the underlying physics governing the discharge and have promising applications in high voltage (HV) transmission engineering.