One problem in Round Robin CPU Scheduling is that if the time required for the running process is slig htly more than time quantum even by a fraction value, th en process gets preempted and context switch occurs . This causes more waiting time for that process and more overheads due to unnecessary context switch. Another problem with RR scheduling is the value of time Quantum. If it is too large, RR algorithm degenerate to FCFS and if it is too short frequent context switches occurs which results into more ove rheads which in turn degrade the performance. In this work a Fuzzy Round Robin scheduling algorithm has been proposed that tries to remove these two problems us ing fuzzy technique. Simulation has been done to compare the performance of this algorithm with its non fuzzy counterpart.