Wireless energy harvesting technique has emerged as a fascinating solution to extend the lifetime of energy constrained networks. However, most of the current researches focus on single antenna network systems, and linear energy harvesting model cannot describe the system harvesting process accurately. Therefore, the multi-user multiple input and multiple output cognitive wireless powered communication system based on energy harvesting network is put forward. With the non-linear energy harvesting model, we establish system throughput optimization model under overlay and underlay scenarios respectively. The problems are generally jointly concave due to the coupled variables and non-linear constraints. To overcome the non-convexity, we convert the problems into equivalent convex forms, and then identify the solutions by applying the Lagrange dual methods. In addition, we also obtain the optimal energy and information transmit covariance matrices respectively, and the optimal time allocation factors. All the solutions’ optimality are proved by mathematical methods theoretically. Finally, the effectiveness and performance of the proposed algorithms are verified based on the actual wind energy harvesting data. Simulation results show that, the optimal algorithm can achieve better average system throughput than the average power allocation algorithm, and the algorithm converges steadily after a finite number of iterations.