The objective of this investigation is to present a semi-analytical method for studying the buckling of the moderately thick composite conical shells under axial compressive load. In order to derive the equilibrium equations of the conical shell, first order shear deformation shell theory is used. The equilibrium equations are derived by applying the principle of minimum potential energy to the energy function that they are in the type of partial differential equations. In the following, the partial differential equations are transformed to algebraic type by using Galerkin and differential quadrature methods and then the standard eigenvalue equation is formed and critical buckling load is calculated. Also, to validate the results obtained in this study, comparisons are made with outcomes of previous literatures and the results of Abaqus finite element software. Analyzing the results, shows the convergence speed and good accuracy of differential quadrature method and desired precision of Galerkin method in calculating the critical buckling load. Finally, the effect of cone angle, fiber orientation, boundary conditions, ratios of thickness to radius and length to radius of the critical buckling load are studied.