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Multiprocessors have become powerful computing means for running real-time applications and their high performance depends greatly on parallel and distributed network environment system. Consequently, several methods have been developed to optimally tackle the multiprocessor task scheduling problem which is called NP-hard problem. To address this issue, this research presents two approaches. The first approach is Modified List Scheduling Heuristic (MLSH). The second approach is hybrid approach which is composed of Genetic Algorithm (GA) and MLSH for task scheduling in multiprocessor system.