Millimeter wave (mmWave) massive MIMO systems will be used extensively in future communications systems to provide high data rates. For such systems, hybrid precoders are preferred to fully digital precoders in decreasing the cost and energy consumption. In this paper, we propose a partially connected hybrid precoding design on the orthogonal matching pursuit (OMP) algorithm. The proposed algorithm accounts for the limitations of analog beamforming circuitry and assumes channel state information (CSI) at both the base and mobile stations. Simulation results show that the proposed algorithm is superior to other solutions in the literature including the nearest Kronecker product (NKP) algorithm and successive interference cancellation (SIC) method. The proposed algorithm provides a higher data rate compared to other methods. In addition, the proposed design offers higher energy efficiency than the fully …