Abstract: Based on Reddy's high-order shear deformation theory, geometrically nonlinear governing equations of composite laminated plates are obtained in the form of displacements by the virtual displacement principle. All five-displacement functions satisfy the boundary conditions that two adjacent edges simply supported and the other two adjacent edges clamped. Galerkin's method is used to transfer non-dimensionalized governing equations to an infinite set of nonlinear algebraic equations. Linear equations of sparse matrix are solved by Biconjugate Gradients Stabilized Method and nonlinear algebraic equations are solved by parameter-regulated iterative procedures. Numerical results of deflection and bending-moment are presented and compared with that of Kirchhoff and Reissner-Mindlin plate theory for different composite materials.