A difference mixed finite element method based on the finite element pair $((P_0×P_1),(P_0×P_1),(P_1×P_0))$$×(P_1×P_1)$ for the three dimensional Poisson equation is studied. The method combines a mixed finite element discretization based on $(P_0, P_0, P_1)×P_1$-element in $(x, y)$-plane and a finite difference discretization based on $(P_1, P_1, P_0) × P_1$-element in $z$-direction. This allows to transmit the finite element solution of the three dimensional Poisson equation in the direction $(x, y, z)$ into a series of finite element solution of the two dimensional Poisson equation in the direction $(x, y).$ Moreover, error estimates for the discrete approximation are derived. Numerical tests show the accuracy and efficiency for the method proposed.