Energy saving and quality of service (QoS) support are two important issues of Long-Term Evolution Advanced (LTE-A) wireless networks. Unfortunately, achieving high energy saving efficiency often implies degradation of QoS support. In this paper, we address the issue of QoS support under Discontinuous Reception (DRX), the power saving mechanism of LTE-A. Different from previous studies which analyzed average packet delay under DRX mechanism, we adopt packet loss ratio due to violation of delay bound as QoS requirements of real-time applications. The problem of QoS support under DRX mechanism is defined as an optimization problem to maximize average power saving under the constraint that the packet loss ratio is no greater than a pre-determined threshold. We derive packet loss ratio and energy saving efficiency given DRX parameter values and propose an approach to select appropriate DRX parameter values. Simulations are conducted to verify our analysis. We found that the analytical results match well with simulations. Moreover, the energy saving efficiency achieved by the selected DRX parameter values is very close to that of the optimum solution.