This paper designs the closed-form precoding matrices for non-regenerative MIMO relay system with the direct link. A multiple power constrained non-convex optimization problem is formulated by using the minimum-mean-squared error (MMSE) criterion. We decompose the original problem into two sub-problems. The relay transceiver Wiener filter structure is first rigorously derived, then the source transmit and destination receive matrices are jointly designed by solving an equivalent dual problem. Through our proposed joint iterative algorithm, the closed-form solutions can be finally obtained. The effectiveness of our proposed scheme is validated by simulations with comparison to some of the existing schemes.