Using the Keldysh nonequilibrium Green function and equation-of-motion technique, we investigate the spin-dependent transport through a closed Aharonov-Bohm interferometer coupled to ferromagnetic leads. With the Fano factor, We analyse the effect of the Fano and the Kondo resonance on the conductance and the variation of the conductance with the spin-polarization strength and the magnetic flux in both the parallel and the antiparallel lead-polarization alignments. Our results show that the conductance can be controlled effectively by the spin-polarization strength and the magnetic flux, while the line shapes of the conductance depend mainly on the magnetic flux and that a large tunneling magnetoresistance and a negative tunneling magnetoresistance can arise by adjusting the relative parameters. This system is a possible candidate for spin valve transistors and is of potential applications in the spintronics.