Abstract: The meshless local Petrov-Galerkin ( MLPG) method is extended to solve the symmetric laminates of fiber-reinforced composite materials using the moving least-square approximation to interpolate solution variables,and the equivalent integral weak form to the governing equation of Kirchhoff’s anisotropic plates.The present method is an effective truly meshless one as it doesn’t need any meshgrids,and all integrals can be easily evaluated over regularly shaped domains and their boundaries.In the analysis,the essential boundary conditions are enforced by a penalty method.Several examples are given and compared with other methods. The result shows that the meshless local Petrov-Galerkin method has a number of advantages such as the quite good accuracy and the high rate of convergence in solving the problems of composite laminated plates.