In this paper, E-polarized electromagnetic scattering problems by a conductive strip grating between a double dielectric layer are analyzed by applying the FGMM(Fourier-Galerkin moment method) known as a numerical method of electromagnetic fileld. The boundary conditions are applied to obtain the unknown field coefficients, and the conductive boundary condition is applied to analysis of the conductive strip. The numerical results for the normalized reflected and transmitted power are analyzed by according as the width and spacing of conductive strip, the relative permittivity and thickness of the double dielectric layers, and incident angles. Generally, as the value of the dielectric constant of the double dielectric layer increases, the reflected power increases and the transmitted power decreases, respectively. As the dielectric constant of the double dielectric layer increases, the current density induced in the strip center increases. The numerical results for the presented structure of this paper are shown in good agreement compared to those of the existing papers.