The quantum time length is usually taken as a fixed value in all applications that use Round Robin (RR) scheduling algorithm. The determination of the optimal length of the quantum that results in a small average turn around time is very complicated because of the unknown nature of the tasks in the ready queue. The round robin algorithm becomes very similar to the first in first served algorithm if the quantum length is large. On the other hand, high context switch results for small values of quantum length which might cause central processing unit (CPU) thrashing this paper we propose a new RR scheduling algorithm based on using neural network models for predicting the optimal quantum length that yields minimum average turn around time. The quantum length is taken to be a function of the service time of the various jobs available in the ready queue. This in contrast to the traditional methods of using fixed quantum length is shown to give better results and to minimize the average turnaround time for almost any collection of jobs in the ready queue.