This paper presents the free vibration analysis of functionally graded carbon nanotube reinforced composite truncated conical panels with general boundary conditions for the first time. Based on the modified Fourier series method for the field variables, the Ritz method is employed to obtain the frequency parameters associated with the mode shapes. The truncated conical panels are reinforced by single-walled carbon nanotubes (SWCNTs) which are assumed to be graded through the thickness direction with different types of distributions. The effective material properties of the FG-CNTRC truncated conical panels are estimated through a micromechanical model based on the extended rule of mixture. In the present study, the artificial spring boundary technique is adopted here to implement the general boundary condition. Several examples are given to demonstrate the convergence, accuracy and flexibility of the present method. The effects of the volume fractions of CNTs, distribution type of CNTs, boundary restraint parameters and geometrical parameters on the vibration behavior of the FG-CNTRC truncated conical panels are presented.