Multilayers consisting of Cu, Co, Cu and Ni(Fe) alloy layers were prepared and magnetoresistance (MR) properties were studied. In the magnetization process, a giant ferrimagnetic state is realized at moderate external field, because of the difference of the coercive fields in the two magnetic layers and then the resistance is greatly enhanced. MR properties were examined by varying the total layer number and the Cu layer thickness. The largest MR ratio was observed in [Cu(55 angstrom)/Co(25 angstrom)/Cu(55 angstrom)/Ni80Fe20(25 angstrom)]x 15; 10% at 300 K and 28% at 80 K.