CPU Scheduling is one of the fundamental concepts of operating system. There exists a number of CPU scheduling algorithms like first come f irst serve, shortest job first scheduling, round robin scheduling, priority scheduling etc. In these algorithms the round robin CPU scheduling is the preferred choice in time shared systems but it is not suitable for Real time systems ,because the existing RR CPU scheduling depends on the choice of static time quantum that decreases the performance of CPU and also have more number of context switches and longer waiting and response time.This in turn leads to low throughput of the system. In a real time systems the process having relatively larger CPU burst time it will leads to the problem of starvation.In this paper we have proposed a new algorithm that gives better CPU performance using the features of shortest job first and round robin scheduling with dynamic time quantum. This algorithm reduces the average waiting time, average turnaround time and number of context switches and also it gives high throughput. The proposed algorithm improves all the disadvantages of simple RR CPU Scheduling algorithm.