This paper presents an optimal design method of high-frequency quenching coil. We have previously reported some optimal design methods of plural permanent magnets with the two- and three-dimensional boundary elements, In this paper, to obtain an optimum coil shape for the purpose of uniform heating, the size modification element is expanded to axisymmetric eddy current problem, The technique is based on the specific element and the least square method, and the coil shape Is modified iteratively, In an example for verification of the convergence, it is shown that our method is useful for the optimization of the high-frequency induction cells.