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Buckling and postbuckling characteristics of laminated graphene-enhanced composite (GEC) truncated conical shells exposed to torsion under temperature conditions using finite element method (FEM) simulation are presented in this study. In the thickness direction, the GEC layers of the conical shell are ordered in a piece-wise arrangement of functionally graded (FG) distribution, with each layer containing a variable volume fraction for graphene reinforcement. To calculate the properties of temperature-dependent material of GEC layers, the extended Halpin-Tsai micromechanical framework is used. The FEM model is verified via comparing the current results obtained with the theoretical estimates for homogeneous, laminated cylindrical, and conical shells, the FEM model is validated. The computational results show that a piece-wise FG graphene volume fraction distribution can improve the torque of critical buckling and torsional postbuckling strength. Also, the geometric parameters have a critical impact on the stability of the conical shell. However, a temperature rise can reduce the crucial torsional buckling torque as well as the GEC laminated truncated conical shell's postbuckling strength.