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Providing efficient resource allocation in the grid computing is a major task. In this paper, a simple and proficient fuzzy based resource allocation algorithm is proposed that not only provides efficient allocation of resources but also ensures high utilization of the resources which are dynamic. The proposed technique constitutes of three different stages namely classification of grid resources, generation of fuzzy rules, and resource allocation based on those fuzzy rules. In the first stage, the grid resource is classified on the basis of dwelling time. In the second stage, the fuzzy rules are developed to allocate the resources to the particular job. In the third & final stage of the technique, the resources are allocated to the submitted jobs based on the generated fuzzy rules. The performance of the proposed algorithm is evaluated on the basis of utilization, failure rate and makespan, and is compared with conventional scheduling algorithms like First Come First Serve (FCFS), Round robin and Random. The results shows that the proposed fuzzy based resource allocation of resource and thereby improving the performance.