Purpose <p>This study presents the vibration nonlinear analysis of functionally graded graphene-reinforced composite (FG-GRC) porous conical shells with axial motion.</p> Methods <p>An improved model is developed to assess the material properties of porous FG-GRCs with different distributions of pores and graphene platelets (GPLs). The nonlinear dynamic equilibrium equations, coupled with the effect of an axial motion, are derived using classical shell theory along with Hamilton’s principle. The Galerkin method is utilized to obtain analytical solutions for both linear and nonlinear frequencies.</p> Results and Conclusion <p>After validating the proposed methodology, the effects of GPLs, internal pores, axial motion, and semi-vertex angle on the frequency, and critical buckling velocity are investigated. The findings reveal that increasing the mass fraction of GPLs tends to enhance the linear frequency and critical velocity. Conversely, higher axial velocity and porosity coefficients lead to decreased frequency. Among the shells with various types of porosity distribution, the linear frequency and critical velocity of those with more pores distributed in the middle area are the highest. The ratio of nonlinear to linear frequency is decreased when the mass volume of GPL increases. However, the ratio is raised when the semi-vertex angle increases. The present method can be applied in analyzing the nonlinear vibration of conical shells, and the results are useful to design the shell structures in various fields, including aerospace, marine, aircraft, and automotive industries.</p>