<p>This paper introduce a new approach for scheduling algorithms which aim to improve real time operating system CPU performance. This new approach of CPU Scheduling algorithm is based on the combination of round-robin (RR) and Priority based (PB) scheduling algorithms. This solution maintains the advantage of simple round robin scheduling algorithm, which is reducing starvation and integrates the advantage of priority scheduling. The proposed algorithm implements the concept of time quantum and assigning as well priority index to the processes. Existing round robin CPU scheduling algorithm cannot be dedicated to real time operating system due to their large waiting time, large response time, large turnaround time and less throughput. This new algorithm improves all the drawbacks of round robin CPU scheduling algorithm. In addition, this paper presents analysis comparing proposed algorithm with existing round robin scheduling algorithm focusing on average waiting time and average turnaround time.</p>