This study proposes a state dependent radio resource scheduling (SDRRS) scheme for downlink traffic to achieve a trade-off among energy saving, quality of service (QoS) satisfaction, and resource utilization in long-term evolution networks. The proposed scheme considers the QoS requirements and channel conditions of the user equipment (UE) and provides high spectrum efficiency. Furthermore, under the QoS constraint, the proposed scheme involves the burst-scheduling concept with respect to transitions between the active and the sleep states to adjust the inactivity timer for optimal energy utilization. Thus, the objective of the SDRRS scheme is to reduce the staying time of the UE in the active mode when the evolved Node B (eNodeB) does not schedule data transfer to it, for energy saving. Exhaustive simulations were conducted using two different traffic models, HTTP and video streaming services, for examining the proposed scheme. The simulation results showed that the proposed scheme achieves considerable energy saving compared with the traditional scheme.