Efficient and Symmetry based precoding plays a key role in wireless communications. In order to improve the transmission performance of multi-user millimeter wave Multiple-Input Multiple-Output (MIMO) (MU-mmWave MIMO) systems, this paper proposes an analog precoding scheme for the receiver of mmWave MIMO with split sub-array hybrid analog and digital architecture. Then, we propose a hybrid analog and digital precoding algorithm based on channel reciprocity (APoCR) to maximize the spectral efficiency by utilizing the triple joint optimization problem, which can be divided into the analog and digital part. The analog combination vectors (ACVs) are obtained by the signal-to-interference-and-noise ratio (SINR) reception maximization of each downlink user and the analog precoding vectors (APVs) are obtained by the SINR reception maximization of each uplink antenna array. The digital precoder of the transmitter is designed after the analog part optimization to alleviate the interference between multiple data streams of the users. The simulation results show that the proposed precoding algorithm has a better sum rate, fast convergence, and improved SINR than the other state-of-the-art algorithms.