We present an iterative method for calculating complex-frequency eigenmodes of photonic crystal slabs with 1D periodicity based on the aperiodic Fourier modal method. By comparison with the known methods, we show that the proposed method is efficient for studying resonant properties of long-period photonic crystal slabs and diffraction gratings. We demonstrate that the method can be used to calculate the eigenmodes of the structures with periods up to at least 500λ. We discuss different aspects of the mode calculation, including convergence of the method, mode field and dispersion analysis. Potential applications of the presented method include investigation of periodic structures with defects and of quasiperiodic and random structures within the super-cell approach.