The main objective of this paper is to introduce a new CPU algorithm called SJRR CPU Scheduling Algorithm which acts as preemptive based on the arrival time. The algorithm helps to improve the average waiting time of Round Robin algorithm in real time uni-processor-multi programming operating system. CPU Scheduling is the basis of multi-programmed operating system. The scheduler is responsible for multiplexing processes on the CPU. There are many scheduling algorithms available for a multi-programmed operating system like FCFS, SJF, Priority, Round Robin etc. The proposed algorithm is based on Round robin scheduling . In this paper, the results of the existing Round Robin algorithm is compared with the proposed algorithm.