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Conventional designs of cognitive radio (CR) multiple-input multiple-output (MIMO) systems mainly focus on the system throughput. Since nowdays the energy efficiency (EE) of wireless systems has become more and more important, this paper intends to improve the system throughput for unit-energy consumption in CR MIMO broadcast channels (BC). The EE optimization problem of CR MIMO BC is studied under the total power constraint, the interference power constraint and the minimum system throughput constraint. Since the EE optimization problem is non-convex, in order to find the optimal solution, we transform it into an equivalent one-dimension problem with a quasi-concave objective function and use the golden section method to solve it. Through simulations, we show the efficiency of the proposed algorithm.