Insertion of a thin nonmagnetic copper Cu(001) layer between the tunnel barrier and the ferromagnetic electrode of a magnetic tunnel junction is shown to result in the oscillation of the tunnel magnetoresistance as a function of the Cu layer thickness. The effect is interpreted in terms of the formation of spin-polarized resonant tunneling. The amplitude of the oscillation is so large that even the sign of the tunnel magnetoresistance alternates. The oscillation period depends on the applied bias voltage, reflecting the energy band structure of Cu. The results are encouraging for the development of spin-dependent resonant tunneling devices.