For providing multimedia streaming services in a mobile WiMAX network, it is important to not only optimize the power consumption of mobile stations (MSs) but also satisfy the QoS requirements of the streams. This paper studies the problem of optimizing the power consumption of the mobile stations (MSs) in the cell of a base station (BS) where each MS has several uplink and downlink connections of real-time services. In order to adapt to heterogeneous delay and jitter requirements of different real-time services, the concept of aperiodic scheduling in is adopted in this paper. In this approach, the MSs wake up by following the pre-allocated transmission schedule given by the BS. The goal of the studied problem is to find an optimal transmission schedule such that the total power consumption can be minimized while the delay and jitter constraints of all connections are still satisfied. In this paper, the integer programming model of the problem is formulated and a lower bound of total power consumption is also derived. Because of its NP-hardness, a heuristic algorithm is proposed to obtain near-optimal solutions. By the numerical results, it is shown that the achieved power consumption of the proposed algorithm is only about 2% higher than the lower bound in the cases where each MS has two UGS and two RT VR connections.