Hybrid precoding achieves a compromise between the sum rate and hardware complexity of millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems. However, most prior works on multi-user hybrid precoding only consider the full-connected structure. In this paper, a novel multi-user hybrid precoding algorithm is proposed for the sub-connected structure. Based on the improved successive interference cancellation (SIC), the analog precoding matrix optimization problem is decomposed into multiple analog precoding sub-matrix optimization problems. Further, a near-optimal analog precoder is designed through factorizing the precoding sub-matrix for each sub-array. Furthermore, digital precoding is designed according to the block diagonalization (BD) technology. Finally, the water-filling power allocation method is used to further improve the communication quality. The extensive simulation results demonstrate that the sum rate of the proposed algorithm is higher than the existing hybrid precoding methods with the sub-connected structure, and has higher energy efficiency compared with existing approaches. Moreover, the proposed algorithm is closer to the state-of-the-art optimization approach with the full-connected structure. In addition, the simulation results also verify the effectiveness of the proposed hybrid precoding design of the uniform planar array (UPA).