In Long Term Evolution (LTE) system, discontinuous reception (DRX) mechanism is widely used as a reliable and effective means of reducing energy consumption. Moving to 5G New Radio, the application scenarios of massive Machine Type of Communication (mMTC) have become increasingly clear, which will support ultra-large-scale device accessing into the network. Therefore, the need for energy efficiency improvement of terminal equipment is becoming more and more urgent under 5G NR. In this paper, a logic controller-based DRX system was proposed to make original DRX more efficient. With logic controller, DRX parameters can be adaptively adjusted by learning the information of historical delay time and packets arrival rate. And then, a better performance of energy conservation will be achieved. Simulation results show the performance improvement of the proposed DRX system.