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Minimax optimization requires to minimize the maximum output in all possible scenarios. It is a very challenging problem to evolutionary computation. In this paper, we propose a surrogate-assisted evolutionary algorithm, Minimax SAEA, for tackling minimax optimization problems. In Minimax SAEA, a surrogate model based on Gaussian process is built to approximate the mapping between the decision variables and the objective value. In each generation, most of the new solutions are evaluated based on the surrogate model and only the best one is evaluated by the actual objective function. Minimax SAEA is tested on six benchmark problems and the experimental results show that Minimax SAEA can successfully solve five of them within 110 function evaluations.