Near real-time periodic tasks, which are popular in multimedia streaming applications, have deadline periods that are longer than the input intervals thanks to buffering. For such applications, the conventional frame-based schedulings cannot realize the optimal scheduling due to their shortsighted deadline assumptions. To realize globally energy-efficient executions of these applications, we propose a novel task scheduling algorithm, which takes advantage of the long deadline period. We confirm our approach can take advantage of the longer deadline period and reduce the average power consumption by up to 18%.