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The main issues in Grid System are performance and Reliability. Achieving high performance Grid Computing requires techniques to efficiently and adaptively allocate tasks and applications to available resources in a large scale, highly heterogeneous, reliable and dynamic environment. Due to operational grid technology which expands the range and scale of grid applications, operational grid systems must exhibit high reliability, thus they must be able to continuously provide correct service. These goals will be made more difficult as grid systems grow in scale, and become more heterogeneous and dynamic in nature. This paper proposes a novel Reliability-Aware Genetic Scheduling Algorithm in Grid environment. This algorithm minimizes Make span, Flow time, and Time To Release as well as it maximizes Reliability of Grid Resources. It takes Transmission time and waiting time in Resource Queue into account. It uses Stochastic Universal Sampling or Rank Roulette Wheel Selection and single Change Mutation to outperform other Genetic Algorithms, speeds up convergence, and provides better solutions than other Genetic Algorithm solutions. Moreover Genetic Algorithm based on Stochastic Universal Sampling has superior solutions over all remaining Genetic Algorithms. The simulation results demonstrates that proposed algorithm reduces total execution time of tasks, increases the Reliability of whole Grid System, and boosts user satisfaction.