The differential integral equation derived from Maxwell's equations was used to rigorously deal with the wavelength- sized surface relief trapezium- shaped reflecting grating in TE (transverse electric) polarization. Numerical analyses of the surface electric field show that the effect of edge and wall of the grating has significant influence on the surface field of metallic materials, e. g. gold and aluminium. Particularly, for the incident wavelength λ=1.0 μm when gold is in strong metallic nature, the edge and wall effect becomes more apparent. The oscillating characteristics of the surface field at the bottom of the grooves and the far field diffraction efficiency against the groove depth are explained by its physical mechanism of the edge and wall effect. This technique can be used to tackle the diffraction problem for arbitrary shapes of grating or single scattering obstacle in arbitrary angles of incidence and polarization.