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This paper addresses the problems in scheduling a precedence constrained tasks of parallel application with random tasks processing time and edges communication time on Grid computing systems so as to minimize the makespan in stochastic environment. This is a difficult problem and few efforts have been reported on its solution in the literature. The problem is first formulated in a form of stochastic scheduling model on Grid systems. Then, a stochastic heterogeneous earliest finish time (SHEFT) scheduling algorithm is developed that incorporates the expected value and variance of stochastic processing time into scheduling. Our rigorous performance evaluation study, based on randomly generated stochastic parallel application DAG graphs, shows that our proposed SHEFT scheduling algorithm performs much better than the existing scheduling algorithms in terms of makespan, speedup, and makespan standard deviation.