In this paper, we design a new type of magnetic tunnel junction (MTJ), which consists of two ferromagnetic layers separated by two adjacent insulating barriers which have different barrier heights and different dielectric constants. Based on the nearly-free-electron approximation, the tunnel current, conductance and magnetoresistance in the double-barrier MTJ are discussed, respectively, by the treatment of the transfer matrix method. Our numerical results show that there exists an asymmetrical tunneling phenomenon in the double-barrier MTJ under the forward and reverse biases, which is modulated by the configuration of magnetizations of two ferromagnetic layers. We predict that our results will stimulate experimental efforts on fabricating the double-barrier MTJ.