To extend user equipment (UE) battery's lifetime, discontinuous reception (DRX) mechanism is employed in Long Term Evolution (LTE) system. In this paper, we propose an analytical model which mainly focuses on the inactivity period. Based on the model, a cost function that considers both energy consumption and response delay is presented. Hence, the target to investigate the proper selection of DRX parameters transforms into a cost minimization problem. We solve the problem with specific constraints. Finally, some numerical results are shown to illustrate that optimizing parameters can make performance improved. By comparing these results, the impact of different parameters on performance is studied.