This paper newly proposes a fast computation technique on the method of image Green's function for p-characteristic calculations, when a plane wave with the transverse wavenumber p is incident on a periodic rough surface having perfect conductivity. In the computation of p-characteristics, based on a spectral domain periodicity of the periodic image Green's function, the image integral equation for a given incidence p maintains the same form for other particular incidences except for the excitation term. By means of a quadrature method, such image integral equations lead to matrix equations. Once the first given matrix equation is performed by a solution procedure as calculations of its matrix elements and its inverse matrix, the other matrix equations for other particular incidences no longer need such a solution procedure. Thus, the total CPU time for the computation of p-characteristics is largely reduced in complex shaped surface cases, huge roughness cases or large period cases.