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The large computing capacity provided by grid systems is beneficial for solving complex problems by using many nodes of the grid at the same time. The usefulness of a grid system largely depends, among other factors, on the efficiency of the system regarding the allocation of jobs to grid resources. This paper proposes an Roulette Wheel Selection Genetic Algorithm using Best Rank Power(PRRWSGA) for scheduling independent tasks in the grid environment. The modified algorithm speeds up convergence and shortens the search time more than IRRWSGA, at the same time the heuristic initialization of initial population using MCT algorithm allow the algorithm to obtain a high quality feasible scheduling solution. The simulation results, show that PRRWSGA has better search time than both IRRWSGA and standard genetic algorithms. Real-world scheduling problems may utilize this algorithm for better results.