In this paper, the buckling analysis of a multilayered composite cylindrical shell which volume fraction of its fiber varies according to power law in longitudinal direction, due to applied compressive axial load is studied. Rule of mixture model and reverse of that are employed to represent elastic properties of this fiber reinforced functionally graded composite. Strain displacement relations employed are based on Reissner-Naghdi-Berry’s shell theory. The displacement finite element model of the equilibrium equations is derived by employing weak form formulation. The Lagrangian shape function for in-plane displacements and Hermitian shape function for displacement in normal direction to the surface of mid-plane are used. Then, finite element code is written in MATLAB based on stated method to obtain the critical axial buckling load. Numerical results show that despite having the same layout and average volume fraction of fibers, the critical axial buckling load of functionally graded composite cylindrical shell is more than that of traditional composite in which the volume fraction of its fiber is constant throughout the shell.