A scheduler for high performance systems containing mixed applications of both real-time multimedia and non real-time applications is proposed. The requirements of our proposed scheduler are twofold, i) all tasks, although the task is a non real-time task with a lower priority, never meet a starvation. ii) any tasks with a higher priority must occupy more CPU resource than any other tasks with lower priority (proportional share scheduler). Although legacy schedulers do not meet the requirements simultaneously, our proposed scheduler effectively satisfies our requirements simultaneously. Our implementation is evaluated with other schedulers such as Multi-level Queue, Multi-level Feedback Queue, and Two-Stage scheduler.