Thermal buckling behavior of truncated conical liner reinforced by laminated composite is investigated in the presence of a general initial imperfection. For this purpose, the method of virtual work and first-order strain-deformation shell theory are employed to extract equilibrium equations. To this end, a finite element code is developed using the 3D 8-node shell element with six degrees of freedom as an analysis tool. Also, the variation of thickness in conical composite shell is considered. Several problems withc-c, s-s, c-f boundary conditions are solved using code to highlight the effect of imperfection size and position. In this way, the most effective imperfection at each boundary condition is determined.