This paper deals with the scattering of a transverse magnetic (TM) plane wave from a perfectly conductive surface with a finite periodic array of rectangular grooves. By use of the method in a previous paper [IEICE TRANS. ELECTRON. VOL.E90-C, no.4, pp.903-906, APRIL 2007], the total scattering cross section is numerically calculated for several different numbers of grooves at a low grazing angle of incidence. It is newly found that, when the corrugation width becomes thousands times of wavelength, the total scattering cross section slightly depends on the groove depth and the period, and becomes almost proportional to square root of the corrugation width with a small correction.