Summary: Auxiliary function methods provide us effective and practical ideas to solve multimodal optimization problems. However, improper parameter settings often cause troublesome effects which might lead to the failure of finding global optimal solutions. In this paper, a minimum-elimination-escape function method is proposed for multimodal optimization problems, aiming at avoiding the troublesome “Mexican hat” effect and reducing the influence of local optimal solutions. In the proposed method, the minimum-elimination function is constructed to decrease the number of local optimum first. Then, a minimum-escape function is proposed based on the minimum-elimination function, in which the current minimal solution will be converted to the unique global maximal solution of the minimum-escape function. The minimum-escape function is insensitive to its unique but easy to adopt parameter. At last, an minimum-elimination-escape function method is designed based on these two functions. Experiments on 19 widely used benchmarks are made, in which influences of the parameter and different initial points are analyzed. Comparisons with 11 existing methods indicate that the performance of the proposed algorithm is positive and effective.