Although millimeter-wave communication technology can meet the design indicators of 5th Generation Mobile Networks (5G)communication, the path loss of millimeter-wave in the transmission process seriously affects its transmission performance. Therefore, waveform shaping technology is needed to concentrate the transmission energy to reduce the impact of path loss. However, the traditional Discontinuous Reception (DRX) mechanism will lead to beam misalignment in the beam shaping system, which is no longer applicable in 5G system. In order to solve the above problems, this research proposes a long-period Adjustable Orientation DRX (A-ODRX) mechanism. The beam search state is merged into the long period state to overcome beam misalignment, and a long period incremental coefficient is introduced to save power consumption. The semi-Markov chain and the European Telecommunications Standards Institute (ETSI) traffic model are used to simulate the A-ODRX mechanism. The average delay, energy saving effect and beam misalignment probability of A-ODRX mechanism are analyzed in simulation. The results show that the A-ODRX mechanism can significantly reduce the beam misalignment probability while effectively reducing the energy consumption of the terminal.