A computationally efficient iterative procedure, the generalized biconjugate gradient fast Fourier transform (BiCG-FFT) method, is presented for analyzing electromagnetic scattering from an arbitrary planar periodic screen. The periodic screen consists of arbitrarily shaped resistive or perfectly conducting patches and homogeneous lossy or lossless dielectric layers. The problem is solved in the spectral domain using the spectral dyadic Green's function that can be obtained via the spectral domain immitance approach. An operator equation is written for the induced surface currents where subdomain rooftop basis functions are chosen to represent these currents. The operator equation is solved by the generalized BiCG-FFT method. Numerical results for the dominant mode reflection and transmission coefficients are presented.