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A cell-based smoothed discrete shear gap method (CS-DSG3) based on the first-order shear deformation theory was recently proposed for static and dynamics analyses of Mindlin plates. In this paper, the CS-DSG3 is extended to the C0-type high-order shear deformation plate theory for the static and free vibration analyses of functionally graded plates (FGPs). In the FGPs, the material properties are assumed to vary through the thickness by a simple power rule of the volume fractions of the constituents. In the static analysis, both thermal and mechanical loads are considered and a two-step procedure is performed including a step of analyzing the temperature field along the thickness of the plate and a step of analyzing the behavior of the plate subjected to both thermal and mechanical loads. The accuracy and reliability of the proposed method is verified by comparing its numerical solutions with those of other available numerical results.