Abstract: The productivity of a computer solely depends on the use of CPU scheduling algorithm in a multi-programmed operating system. In this study a new variant of priority scheduling algorithm has been proposed to reduce the average waiting time as well as the average turnaround time of the processes. It is observed that in existing priority scheduling algorithm the average waiting time and average turnaround time is very high for the processes, which have equal priority. But the proposed upgrading of this study can handle priority-scheduling algorithm with much more reduced waiting time and turnaround time for the processes.