In the present study, a theoretical solution for thermomechanical creep analysis of functionally graded (FG) thick cylindrical pressure vessel with variable thickness based on the first-order shear deformation theory (FSDT) and multilayer method (MLM) is presented. To the best of the researchers’ knowledge, in the literature, there is no study carried out into FSDT and MLM for creep response of cylindrical pressure vessels with variable thickness under thermal and mechanical loadings. The vessel is subjected to a temperature gradient and nonuniform internal pressure. All mechanical and thermal properties except Poisson’s ratio are assumed to vary along the thickness direction based on a power-law function. The thermomechanical creep response of the material is described by Norton’s law. The virtual work principle is applied to extract the nonhomogeneous differential equations system with variable coefficients. Using the MLM, this differential equations system is converted into a system of differential equations with constant coefficients. These set of differential equations are solved analytically by applying boundary and continuity conditions between the layers. In order to verify the results of this study, the finite element method (FEM) has been used and according to the results, good agreement has been achieved. It can be concluded that the temperature gradient has significant influence on the creep responses of FG thick cylindrical pressure vessel.