In Ni-Fe/Cu multilayers formed by ion beam sputtering, oscillatory magnetoresistance changes with copper thickness have been observed at room temperature. As the thickness of the Ni-Fe layer increased, the magnetoresistance ratio increased, reached a maximum value at 1.0 - 1.1 nm, and decreased slightly above 1.1 nm. The maximum magnetoresistance ratio was 19% for the Ni-Fe(1.0 nm)/Cu(1.0 nm) multilayer at room temperature.