How to enhance the Machine-to-Machine (M2M) communication with improved software services becomes an essential issue in the future fifth generation (5G) systems. Considering the enormous number of connected devices located in a specific direction relative to the base station, Millimeter-Wave (mmWave) communication with the beamforming technology plays a crucial role in meeting the high data transmission requirements of the devices. To achieve the requirements, it is necessary for the devices to integrate the Discontinuous Reception (DRX) mechanism with the mmWave communication. We propose a Beam-Aware DRX mechanism that is adaptive to a periodic beam pattern in mmWave communication. Compared with the original LTE DRX mechanism in mmWave communication.