n this paper, we study the problem of optimizing the weighted total system rate (WSR) for a downlink broadcast communication system using multiple input-multiple output (MIMO) antenna technology, wherein a Base station (BS) transmits multiple data streams simultaneously to K multi-antenna MIMO mobile stations (MSs). Upon the power constraint, the optimal solution is to find the pre-coding matrices at the BS and the decoding matrices at the MSs. However, this type of optimization problem is usually nonlinear and non-convex, so it is relatively difficult to solve by analytical methods. To tackle the problem, we propose a novel algorithm to optimize the WSR of the system based on the Harris Hawking Optimization (HHO) algorithm using the linear least squares mean error (MMSE) filter at the MSs. Numerical results have been used to demonstrate the outperformance of the proposed algorithm, comparing with existing methods such as Block Diagonalism with Waterfilling algorithm and Particle Swarm Optimization, particularly at the low signal-to-noise (SNR) range. In the end, we may propose an adaptive method that combines the advantages of different algorithms at various SNR domains to maximize the system performance.