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Task Graph Scheduling is an NP-Hard problem. In this paper a new hybrid method based on Genetic Algorithm and Learning Automata is proposed. The hybrid method begins with an initial population of randomly generated chromosomes. A chromosome is Equal to learning automaton.Each Chromosome by itself represents a stochastic scheduling.The scheduling is optimized within a learning process.Compared with current genetic approaches to DAG scheduling better results are achieved. The main reason underlying this achievement is that an evolutionary approach such as genetics, looks for the best chromosomes within genetic populations whilst in the approach presented in this paper hybrid algorithm is applied to find the most suitable position for the genes and looking for the best chromosomes too. The scheduling resulted from applying our hybrid algorithm to some benchmark task graphs are compared with the existing ones