Magneto transport of carriers with a spin-dependent gap in a ferromagnetic-gated bilayer of graphene is investigated. We focus on the effect of an energy gap induced by the mismatch of the exchange fields in the top and bottom layers of an AB-stacked graphene bilayer. The interplay of the electric and exchange fields causes the electron to acquire a spin-dependent energy gap. We find that, only in the case of the anti-parallel configuration, the effect of a magnetic-induced gap will give rise to perfect spin filtering controlled by the electric field. The resolution of the spin filter may be enhanced by varying the bias voltage. Perfect switching of the spin polarization from+100%to?100%by reversing the direction of electric field is predicted. Giant magnetoresistance is predicted to be easily realized when the applied electric field is smaller than the magnetic energy gap. It should be pointed out that the perfect spin filter is due to the layer-dependent exchange energy. This work points to the potential application of bilayer graphene in spintronics.