This paper extends the use of the hierarchic degenerated shell element to geometric non-linear analysis of composite laminated skew plates by the p-version of the finite element method. For the geometric non-linear analysis, the total Lagrangian formulation is adopted with moderately large displacement and small strain being accounted for in the sense of von Karman hypothesis. The present model is based on equivalent-single layer laminate theory with the first order shear deformation including a shear correction factor of 5/6. The integrals of Legendre polynomials are used for shape functions with p-level varying from 1 to 10. A wide variety of linear and non-linear results obtained by the p-version finite element model are presented for the laminated skew plates as well as laminated square plates. A numerical analysis is made to illustrate the influence of the geometric non-linear effect on the transverse deflections and the stresses with respect to width/depth ratio (a/h), skew angle (${eta}$), and stacking sequence of layers. The present results are in good agreement with the results in literatures.