Massive multiple input multiple output (MIMO) technology is a key enabler of the next generation wireless communications. The partially-connected hybrid beamforming architecture is attractive in massive MIMO systems for its reduced cost, power consumption, and hardware complexity. On the other hand, the specific analog beamforming structure and finite-resolution in phase shifters complicate the beamforming design. In this paper, we study the hybrid beamforming design for the partially-connected architecture, where users can have multiple antennas and different requirements on quality of service (QoS). A transmit power minimization problem is formulated. The beamforming design needs to be aligned to discrete phase values due to the practical limitations. Such problem is non-convex and is hard to solve. We propose an effective algorithm for this problem. In particular, the penalty-based method is used to decouple the variables. The original problem is decomposed into several sub-problems. The block prox-linear method is applied to solve the sub-problems alternatively with convergence guarantee. We show the effectiveness and robustness of our proposed algorithm via simulations. Our proposed algorithm with low resolution phase shifters achieves better performance with lower transmit power than existing methods.