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An efficient discontinuous Galerkin time-domain (DGTD) method with an implementation of generalized periodic boundary conditions (PBCs) is proposed to analyze the electromagnetic scattering from arbitrary skewed periodic structures. The transformed field variable approach and the discontinuous Galerkin technique with nonconformal mesh are presented to implement the generalized PBCs for arbitrary skewed periodic structures under both normally and obliquely incident illuminations. The arbitrary high-order time-stepping scheme, which retains the DGTD feature of high-order accuracy and breaks the Butcher barrier, is extended to a transformed version of Maxwell’s equations introduced by the generalized PBCs implementation. The proposed method enables an efficient modeling of arbitrary skewed arrays with a fixed unit-cell mesh. Numerical examples for skewed periodic structures, such as an infinite gold film, 1-D and 2-D staggered dipole frequency-selective surfaces (FSSs), mechanically reconfigurable FSSs, and skewed nanohole arrays, are presented to demonstrate the accuracy and applicability of the proposed method. [ABSTRACT FROM AUTHOR]