In the Long Term Evolution (LTE) system, Discontinuous Reception (DRX) has been introduced for power saving to extend the battery life of the User Equipment (UE). In this thesis, we take an overview of the DRX mechanism and further analysis the mechanism with bursty packet traffic model. We propose a scheme for DRX Cycle adjustment to enhance the power saving performance in different traffic conditions. Based on the analytical model, effects of the DRX parameters on the packet delay performance are also investigated. Simulation results show that the scheme can reduce the power consumption with satisfying the packet delay requirement and a trade-off relationship between power saving and packet delay performance.