|This paper considers an energy-efficient, hybrid digital, and analog precoding design problem in millimeter-wave massive multiple-input multiple-output systems, in which the analog precoder is realized with a small number of energy-efficient switches and inverters rather than with a large number of highresolution phase shifters. However, finding the optimal weights of such energy-efficient hybrid precoding requires solving a challenging combinatorial problem. A known solver, namely “adaptive cross-entropy (ACE),”can provide a reasonable solution but its computational complexity is still high. Thus, a simple yet effective coordinate update algorithm (CUA) is proposed in this paper to reduce the computational complexity while maintaining and even improving the achievable rate performance. In addition, we propose a new hybrid precoding architecture that introduces the antenna selection mechanism into the conventional energy-efficient-based hybrid precoding architecture to further reduce energy consumption. Although, the resulting design problem of this new architecture becomes more complex in that the traditional ACE-based solver cannot be applied directly, the proposed CUA-based solver can still handle this problem. The simulation results demonstrate that the proposed CUA-based solver provides the same or even an improved achievable rate performance than the ACE-based solver at a lower complexity. Furthermore, the energy consumption of the proposed hybrid precoding architecture is lower than that of the conventional energy-efficient hybrid precoding architecture.