In computational Grid, fault tolerance is an imperative issue to be considered during job scheduling. Due to the widespread use of resources, systems are highly prone to errors and failures. Hence fault tolerance plays a key role in grid to avoid the problem of unreliability. The two main techniques for implementing fault tolerance in grid environment are check pointing and replication. This paper proposes a replication technique to improve the fault tolerance of the fittest resource scheduling algorithm. Scheduling the task to the appropriate resource is a vital requirement in computational Grid. The fittest resource scheduling algorithm searches for the appropriate resource based on the job requirements, in contrary to the general scheduling algorithms where jobs are scheduled to the resources with best performance factor.