In this paper, we propose an efficient algorithm to schedule real-time multimedia tasks for streaming MPEG-2 video clips. In our task model, each frame is decoded by a separate multimedia task whose priority is decided based on the precedence and importance of the corresponding frame in the video stream. We develop a priority-driven scheduling policy in order to effectively allocate the CPU bandwidth to multimedia tasks for MPEG-2 decoding. We show how to dynamically control the fraction of the allocated bandwidth according to the priority. The goal of the proposed scheduling method is to minimize the number of decoding tasks that have missed their deadlines while reducing the decoding times of these multimedia tasks. The performance of this scheduling method is compared against that of a similar technique with no priority scheme through simulation experiments.