In the previous report, we studied on the inverse acoustic scattering problem for shape identification. The inverse problem under consideration is to determine the shape of an obstacle in the fluid from a knowledge of the time-harmonic incident wave and the far field pattern of the scattered wave. We inrtoduced a numerical method for inverse scattering problem for shape identification and showed some numerical examples. In this report, we introduce new integral equations which is based on the relation between the small modification of the boundary shape and sound scattering field and can compute efficiently than the previous report method. Using the integral equations and Schiffer's theorem, a numerical method for inverse acoustic scattering problem is presented. Numerical examples are given showing the practicality of the method.