Estimating the upper bound of maximum prediction errors can be achieved by using the conditional nonlinear optimal perturbation(CNOP).Generally, CNOP is obtained by the constrained optimization algorithm based on gradient information provided by the associated adjoint model.However, when the nonlinear model contains discontinuous "on-off" switches, the conventional adjoint method cannot provide the correct gradient direction, and eventually induces the optimization to fail.Hence, genetic algorithm (GA) with self-adaptive mutation and blend crossover operators, tournament selection mechanism and niche strategy are adopted to solve the upper bound of maximum prediction errors in this paper.In order to test the effectiveness of the new method, we take the modified Lorenz model as the prediction model, and make comparison between the new method and the conventional adjoint method respectively aiming to three different initial reference states.The numerical experiment results show that the new method is more effective for solving the upper bound of maximum prediction errors.