We study the characteristics of the spin-tunneling time and the transmission coefficient in a ferromagnetic/semiconductor/ ferromagnetic heterojunction with a δ tunnel barrier. The effects of the quantum size and Rashba spin-orbit coupling are discussed. It is shown that the existence of the tunnel barrier will reduee the magnitude of the transmission coefficient and the variation of the barrier strength will change the phase of the transmission coefficient. The oscillation frequency of the transmission coefficient increases with the increasing of the Rashba spin-orbit coupling. When the spin-dependent electron tunnels through the heterojunction, the tunneling time becomes longer with the length of the semiconductor increasing. The Rashba spin-orbit coupling also affects the spin-tunneling time.