This paper studies energy-efficient hybrid beamforming architectures and its algorithm design in millimeter-wave communication systems, aiming to address the challenges faced by existing hybrid beamforming due to low hardware flexibility and high power consumption. To solve the problems of existing hybrid beamforming, a novel energy-efficient hybrid beamforming architecture is proposed, where radio-frequency (RF) switch networks are introduced at the front and rear ends of the phase shifter network, enabling dynamic connections between the RF chains and the phase shifter array as well as the antenna array. The system model of the proposed architecture is established, including digital precoding and analog precoding processes, and the practical hardware limitations such as quantization errors of the digital-to-analog converter (DAC) and phase shifter resolution. In order to maximize the energy efficiency, this paper derives an energy efficiency model including spectral efficiency and system power consumption, and a hybrid precoding algorithm is proposed based on block coordinate descent to iteratively optimize the digital precoding matrix, analog precoding matrix, and DAC resolution. Simulation results under the NYUSIM-generated millimeter-wave channels show that the proposed hybrid beamforming architecture and precoding algorithm have higher energy efficiency than existing representative architectures and precoding algorithms under complete and partial channel state information, while the loss of spectral efficiency compared to fully connected architecture is less than 20%