Abstract Millimeter-wave MIMO will use hybrid precoding to improve the spectral efficiency. In this paper, we propose a spectral efficient hybrid precoding algorithm. In order to maximize the projection of hybrid precoding matrix on the optimal precoding matrix, we design the analog precoding matrix by selecting an optimal combination from the candidate matrix. Then, we regard the channel matrix and the obtained analog precoding matrix as an equivalent channel matrix, and use regularized zero-forcing to acquire the digital precoding matrix. Finally, we present simulation results of the proposed hybrid precoding algorithm and show that the algorithm approaches the optimal precoding.