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Dependent tasks scheduling in grid environment is a NP-complete problem. Convergence in the accuracy for conventional GA is better than other scheduling algorithms, but the speed of convergence is too slow in a realistic scheduling. In view of this situation, this paper presents a hybrid adaptive genetic algorithm (HAGA) which can improve the local search ability by adding the adjustment for the specific problem, so it has good global and local search ability. At the same time, in order to avoid such disadvantages as premature convergence, low convergence speed and low stability, the algorithm adjusts the crossover and mutation probability adaptively and nonlinearly. Experiments show that the presented algorithm not only improves the speed of convergence, but also improves the accuracy of convergence.