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Grid computing solves high performance and high-throughput computing problems through sharing resources ranging from personal computers to super computers distributed around the world. As the grid environments facilitate distributed computation, the scheduling of grid jobs has become an important issue. In this paper, an investigation on implementing Multiobjective Variable Neighborhood Search (MVNS) algorithm for scheduling independent jobs on computational grid is carried out. The performance of the proposed algorithm has been evaluated with Min–Min algorithm, Simulated Annealing (SA) and Greedy Randomized Adaptive Search Procedure (GRASP) algorithm. Simulation results show that MVNS algorithm generally performs better than other metaheuristics methods.