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Seeking the optimal strategy of a multi-reservoir system is an important approach to develop hydropower energy, in which the Genetic Algorithm (GA) is commonly used as an effective tool. However, when the traditional GA is applied in solving the problem, the constraints of water balance equation, hydraulic continuity relationship and power system load demand might be violated by the crossover and mutation operator, which decreases the efficiency of the algorithm in searching for a feasible region or even leads to a convergence on an infeasible chromosome within the expected generations. A modified GA taking stochastic operators within the feasible region of variables is proposed. When determining the feasible region of constraints, the progressive optimal approach is applied to transform constraints imposed on reservoirs into a singular-reservoir constraint, and a joint solution with consideration of adjacent periods at crossover or mutation points is used to turn the singular-reservoir constraints into singular variable constraints. Some statistic indexes are suggested to evaluate the performances of the algorithms. The experimental results show that compared to GA adopting a penalty function or pair-wise comparison in constraint handling, the proposed modified GA improves the refinement of the quality of a solution in a more efficient and robust way.