Abstract. Grid computing is a computing framework to meet the growing computational demands. This paper introduces a novel approach based on Particle Swarm Optimization (PSO) for scheduling jobs on computational grids. The representations of the position and velocity of the particles in the conventional PSO is extended from the real vectors to fuzzy matrices. The proposed approach is to dynamically generate an optimal schedule so as to complete the tasks within a minimum period of time as well as utilizing the resources in an efficient way. We evaluate the performance of the proposed PSO algorithm with Genetic Algorithm (GA) and Simulated Annealing (SA) approaches.