Based on the transfer matrix method and the quantum coherent transport theory of Mireles and Kirczenow, the effects of the Rashba spin-orbit coupling and the spin-filter on the electronic transport properties in the NM/FS1/I/FS2/NM（NM represents the nonmagnetic metal layer, I represents the nonmagnetic insulator layer, and FS represents the magnetic semiconductor layer）double spin-filter tunnel junction are investigated. The influence of thickness of insulator layer and magnetic semiconductor layer on the tunnel magnetoresistance （TMR） and conductance are studied for different Rashba spin-orbit coupling strength and the different angle θ between the two magnetic moments of the left and right magnetic semiconductor layer. The results indicate that: in the presence of the spin-filter effect and the Rashba spin-orbit coupling interaction in the magnetic semiconductor layer, large TMR can be obtained in this double spin-filter junction. With the strength of Rashba spin-orbit coupling increasing, the tunnel magnetoresistance and conductance exhibit rapidly oscillating behavior and the oscillation period decreases gradually.