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Grid computing allows one to unite pools of servers, storage systems, and networks from different domain with their specific management policies, into a single large system. The Grid Environment is dynamic and its domains act autonomously. Unfortunately, in such an environment failure may occur occasionally or a volatile host can delay the entire execution for a long period of time, which in turn can fail taskpsilas execution. In this paper, a Novel Fault-tolerant Particle Swarm Optimization Scheduler (NFPSO) is suggested to schedule independent tasks. This approach aims to generate a scheduling plan to overcome the resource failure problem while it decreases total taskpsilas completion time, cost and the percentage of Unsuccessful scheduled task. The experimental results of NFPSO scheduler are compared with results of Genetic Algorithm, Simulated Annealing, mountain Climbing and a Random scheduler. NFPSO shows better result in cost and success rate criteria than all other, but in completion time criteria GA has better than our proposed algorithm which is better than other.