This paper deals with the diffraction of a transverse magnetic (TM) plane wave by a perfectly conductive periodic surface by an integral method. However, it is known that a conventional integral method does not work for a critical angle of incidence, because of divergence of a periodic Green's function (integral kernel). To overcome such a divergence difficulty, we introduce an image Green's function which is physically defined as a field radiated from an infinite phased array of dipoles. By use of the image Green's function, it is newly shown that the diffracted field is represented as a sum of radiation from the periodic surface and its image surface. Then, this paper obtains a new image integral equation for the basic surface current, which is solved numerically. A numerical result is illustrated for a very rough sinusoidal surface. Then, it is concluded that the method of image Green's function works practically even at a critical angle of incidence.