This paper presents a new energy-aware QoS scheduling and call admission control algorithm for WiMAX IEEE 802.16e wireless access standard. The scheduling algorithm works at MAC layer and is designed towards minimizing power consumption at mobile stations supporting multiple Unsolicited Grant Service (UGS) connections, while meeting the QoS requirements of the connections. The algorithm uses a novel idea to fill an active OFDM frame as much as possible in order to increase the number of OFDM frames in sleep mode at mobile station. The algorithm also considers the dynamic nature of connection joining and termination. We used Voice-over-IP (VoIP) traffic connection models for UGS traffic flows to simulate and validate algorithm. The simulation model was tested using VoIP codec types with different rates and QoS requirements. Simulation results show that a power saving in the range of 50–75% can be easily achieved at the mobile station under low-to-moderate traffic intensities.