In this letter, we propose a hybrid precoding design algorithm by utilizing RF chain selection to optimize the number of RF chains to achieve high energy efficiency (EE) with slightly spectral efficiency (SE) performance degradation. In this algorithm, we firstly reformulate the energy efficiency optimization problem, and resolve the hybrid precoding optimization problem with alternating minimization method to seek the approximate optimal analog precoder and digital precoder under the proposed structure. Then, we perform the transmitter RF chain selection to find the optimal RF chain set corresponding to better EE and SE performance. Simulation results show the proposed algorithm achieves the good trade-off between EE and SE performance when the transmit power constraint is no larger than 30 dBm.