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An efficient finite-difference time-domain (FDTD) algorithm with a simple periodic boundary condition (PBC) is developed to analyze general periodic structures with arbitrary skewed grids. The algorithm is easy to implement and efficient in both memory usage and computation time. The stability criterion of the algorithm is angle independent and therefore it is suitable for implementing incidence with angle close to grazing as well as normal incidence. The validity of this algorithm is verified through several numerical examples such as dipole and Jerusalem cross frequency selective surfaces (FSS) with various skew angles.