High-frequency radio wave diffraction by a perfectly conducting arbitrarily shaped smooth surface is considered analytically. The results of solving the integral equation for surface currents at a gentle surface, when multiple scattering and surface shadowing can be neglected, are presented. The diffraction corrections to GO values of the surface currents were obtained (up to the second order of the small parameter ∼1/k, where k is the wave number of the incident EM wave) depending on the local angle of incidence, surface curvatures, and their space derivatives. It is shown that diffraction caused by the local surface curvature results not only in small corrections to the GO currents, but also gives rise to the surface current components orthogonal to those induced by the incident wave in the local GO limit. These general results are applied to the specific problem of backscattering from a Gaussian statistically rough surface at normal incidence. The diffraction corrections to the GO statistically averaged backscattering cross sections, HH/VV polarization ratio (which is equal to unity in the GO limit) and cross-polarization coefficient are obtained as functions of the 2nd (surface slope variances) and 4th (surface curvature variances) moments of the surface roughness power spectra. It is shown that diffraction results in the appearance of the cross-polarized component in the backscattered field, which is equal to zero in the GO limit.