Abstract: In this paper, the optimal precoder is designed for simultaneous wireless information and power transfer in MIMO systems with the mean channel state information. The objective of the precoder design is to maximize the expected system information rate, meanwhile meeting the minimum energy requirement of the energy receiver. We formulate the problem as a semi-definite programming (SDP), further transform it into a dual problem, and prove the two problems are equivalent. Based on the technique of covariance matrix decomposition, we transform the constrained optimization problem into an unconstrained one and propose a gradient-decent searching method to solve this problem. Besides, we also provide a lemma on the boundary of the achievable rate-energy (R-E) region, in which two important boundary points are provided. Computer simulation has been deployed to demonstrate the convergence of the proposed precoding algorithm and present achievable R-E regions under a few system settings. The results show that, the proposed method has much broader R-E regions, in comparison with a few classical transmission schemes.