In this paper topology optimization of the periodic structure of sub-wavelength hole array that have specified optical characteristics is presented. The research of sub-wavelength hole array in an opaque metal film attracted many researchers by its special transmission spectrum. Such special transmission spectrum is induced by combination of coupling of evanescent wave and propagated wave and surface plasmon resonance. Recently, it was reported that the transmission spectrum can be changed not only by size and periodicity of hole array, but also by shape of hole. However, the systematic design method of hole array structure for desired transmission spectrum is yet not proposed. Here, we propose topology optimization method to design hole array structure to obtain desired optical characteristics.