In this paper, electromagnetic scattering problems by a resistive strip grating with zero resistivity at the strip-edges on a grounded 2 dielectric layers according as strip width and spacing, relative permittivity, thickness of dielectric layers, and incident angles of a electric wave are analyzed by applying the FGMM(Fourier-Galerkin Moment Method) known as a numerical procedure. The scattered electromagnetic fields are expanded in a series of floguet mode functions. The boundary conditions are applied to obtain the unknown field coefficients and the resistive boundary condition is used for the relationship between the tangential electric field and the electric current density on the strip. The tapered resistivity of resistive strips varies zero resistivity at strip edges. Then the induced surface current density on the resistive strip is expanded in a series of Chebyshev polynomials of the second kind. The normalized reflected power with zero resistivity in this paper show in good agreement with those of existing paper.