Conical shells are widely used in various engineering applications such as mechanical, civil and aerospace engineering. In the present paper, based on the first order shear deformation theory (FSDT) of shells, the nonlinear vibration behavior of truncated conical shells with different boundary conditions is investigated using a numerical approach. To this end, the governing equations of motion and corresponding boundary conditions are derived by the use of Hamilton's principle. After catching the dimensionless form of equations, the generalized differential quadrature (GDQ) method is employed to obtain a discretized set of nonlinear governing equations. Thereafter, a Galerkin-based scheme is applied to achieve a time-varying set of ordinary differential equations and a method called periodic grid discretization is used to discretize the equations on the time domain. The pseudo arc-length continuation method is finally applied to obtain the frequency-amplitude response of conical shells. Selected numerical results are presented to examine the effects of different parameters such as thickness-to-radius ratio, small-to-large edge radius ratio, semi-vertex angle of cone, circumferential wave number and boundary conditions. It is concluded that the changes of the vibrational mode shapes and circumferential wave number have significant effects on the nonlinear vibration characteristics and hardening effects.