The 3GPP Long Term Evolution (LTE) wireless technology provides high data rates and improved latency to the end users. Such improvement is obtained from the advanced MAC and PHY layer techniques, which exhaust the battery life of the User Equipment (UE) quickly. To save the power of UE, 3GPP LTE proposes a mechanism called Discontinuous Reception Mechanism (DRX) which lets the UE switch its RF module off when data needs not be transmitted. In this paper, we have developed an analytical model to derive the DRX power saving obtained by the UE in LTE system. Different from other work, the RRC (Radio Resource Control) states transition is considered. The time period for power saving operation is divided into several independent parts to derive the power consumption and the transmission delay. In addition, we introduce the real power consumption model into the derived power saving model to obtain the truly power consumption. The analytical results show the UE with lower packet arrival rate can effectively save more power when entering RRC-IDLE state, and there is a trade-off between the power consumption and the transmission delay.