Discontinuous reception (DRX) is supported in 3GPP Long Term Evolution (LTE) to reduce power consumption of user equipments (UEs). Power conservation achieved via DRX can be further increased with a packet scheduler that takes DRX states into consideration. Thus, in addition to quality of service (QoS) and fairness factors, which have been the main focus so far in scheduler design, energy efficiency must also be considered in scheduling. In this paper, we introduce a DRX and QoS-aware uplink packet scheduling algorithm (DQEPS) for LTE networks. One of the main reasons of poor DRX utilization is the continuous uplink packet traffic generated by applications working in the background. Accordingly, we first lay out the cumulative distribution functions (CDF) of interpacket arrival durations constructed by inspecting uplink packet transmission for various applications. Then, we form metrics for each bearer using these CDFs along with the DRX states, QoS parameters, channel conditions, and the buffer status of the bearers. Using these metrics, we develop a scheduling algorithm for the uplink, which aims to maximize power conservation of DRX mechanism by scheduling packets in a way that tries to minimize ON duration, while meeting the QoS requirements. Performance evaluations indicate that DQEPS reduces power consumption significantly compared to the previously proposed methods for LTE.