In this study, a polygonal finite element method (PFEM) is extended and combined with the C0-type higher-order shear deformation theory (C0-HSDT) for the static and free vibration analyses of laminated composite plates. Only the piecewise-linear shape function which is constructed based on sub-triangles of polygonal element is considered. By using the analogous technique which relies on the sub-triangles to calculate numerical integration over polygonal elements, the procedure becomes remarkably efficient. The assumption of strain field along sides of polygons being interpolated based on Timoshenko's beam leads to the fact that the shear locking phenomenon can be naturally avoided. In addition, the C0-HSDT theory, in which two additional variables are included in the displacement field, significantly improves the accuracy of the displacements and transverse shear stresses. Numerical examples are provided to illustrate the efficiency and reliability of the proposed approach.