This paper deals with the wave scattering from a periodic surface with finite extent. Modifying a spectral formalism, we find that the spectral amplitude of the scattered wave can be determined by the surface field on only the corrugated part of the surface. The surface field on such a corrugated part is then expanded into Fourier series with unknown Fourier coefficients. A matrix equation for the Fourier coefficients is obtained and is solved numerically for a sinusoidally corrugated surface. Then, the angular distribution of the scattering, the relative power of each diffraction beam and the optical theorem are calculated and illustrated in figures. Also, the relative powers of diffraction are calculated against the angle of incidence for a periodic surface with infinite extent. By comparing a finite periodic case with an infinite periodic case, it is pointed out that relative powers of diffraction beam are much similar in these of diffraction for the infinite periodic case.