In this paper, we construct a ferromagnet/semiconductor/ferromagnet parabolic well magnetic tunneling junction with double barriers as research object by inserting another semiconductor as a barrier between ferromagnetic and semiconductor potential wells. On the basis of the quantum coherent transport theory and transfer matrix method, we investigate the spin polarized electron transport and the tunnel magnetic resistance (TMR) in parabolic well magnetic tunneling junction with double barriers. We derive the analytical expressions of transmission probability, tunnel magnetic resistance and spin polarization from the new magnetic tunneling junction mode. The significant quantum size, Rashba spin orbit interaction, the angle effect and the thickness of the double barriers layer are discussed simultaneously. The results indicate that the tunnel magnetic resistance shows periodic variation as the width of the parabolic-well at different angles. The TMR is monotonically decreasing when the angle varying from 0 to up, which reflects the structure of the spin valve effect. Meanwhile, results also show that the spin polarization and the tunnel magnetic resistance oscillate with the same period for different barriers thickness. The phase difference appears after inserting the barriers. With increasing the barriers width, phase difference becomes large. The amplitude and peak to alley ratio of the spin polarization and the tunnel magnetic resistance are increase with the barrier width increases. Furthermore, the spin polarization make quasiperiodic oscillation that the oscillation amplitudes become large, the period and peak to alley ratio are decrease as the Rashba spin-orbit coupling strength increases. It appears the spin flip phenomenon as increasing the thickness of the barriers. The TMR shows the typical properties of resonant tunneling with the increasing of the spin orbit coupling strength. In order to better reveal the role of the symmetry double tunnel barriers in the parabolic well structure, we calculate TMR against the thickness of the double barriers. It is found that the existence of the double tunnel barriers increase the TMR and the spin polarization significantly, which shows that the large TMR value can be obtained with the suitable layer thickness of the double barriers layer and the Rashba spin-orbital coupling coefficients. These characteristics are helpful to promote the development and application of new magnetic tunnel junctions.