We investigated the spin-dependent transmission coefficient and tunneling magnetoresistance in symmetric parabolic-well with two ferromagnetic contacts (F/SPW/F). The quantum size effect and Rashba spin-orbit interaction are discussed simultaneously. The results indicate that the transmission coefficient and tunneling magnetoresistance are periodic function of the parabolic-well width. The oscillation frequencies of the transmission coefficient and tunneling magnetoresistance decrease with the increasing of the parabolic-well depth. The oscillation frequencies of the transmission coefficient and tunneling magnetoresistance increase with the increasing of the Rashba spin-orbit coupling strength. The amplitude and peak-to-valley ratio of the transmission coefficient and tunneling magnetoresistance are strongly dependent on the difference in orientations of the two magnetizations in the left and right ferromagnets.