In this paper, we investigate the widely linear precoding (WLP) design for the multi-user Multiple-input Multiple-output broadcast channel (MIMO BC). Our goal is to maximize the weighted sum-rate (WSR) under the constraint of the total power of base station. However, such the maximum WSR problem is not convex. We transform it to a minimum weighted meansquare error (WMSE) problem. Further, we propose the block coordinate descent (BCD) method with alternate optimization to calculate each paired-set of variables, and then obtain the stationary point of the pre-coding matrix at the transmitter and estimation matrix at the receiver by iterative computation. Finally, we analyze the convergence property and simulation experiments are conducted to verify the results. Results show that the sum-rate based on the widely linear model is larger than that on the conventional linear model.