We investigate the transport properties through magnetic superlattices with asymmetric double-barrier units in monolayer graphene. In N-periodic asymmetric double-barrier units, there is (N−1)-fold resonant peak splitting for transmission, but the splitting is (2N−1)-fold in N-periodic symmetric units. The transmission depends not only on the value of incident wavevectors but also on the value and the direction of transverse wavevectors. This renders the structure's efficient wavevector filters. In addition, the conductance of standard electrons with a parabolic energy spectrum is suppressed more strongly than that of Dirac electrons, whereas the resonances are more pronounced for Dirac electrons than for standard ones.