Based on the transfer-matrix method, we investigated the spin transport through a graphene-based nanostructure with effective exchange field. It is found that the effective exchange field induces a spin-dependent Klein tunneling. The magnetoresistance becomes a number of times larger than that in the case of the Rashba spin-orbit interaction. With increasing the effective exchange field strength, the magnetoresistance and the Fano factor exhibit periodic oscillation features. In graphene superlattice, when the effective exchange field satisfies a certain condition, the Fano factor can be tuned from nearly zero to 1/3 by applying an appropriate periodic gate voltage.