Abstract: This paper numerically studies the long-time dynamic behavior of the cubic nonlinear Klein-Gordon equation with weak nonlinear terms by using Crank-Nicolson pseudo-spectral method, and establishes the optimal error estimate of the scheme. According to the error estimate, the optimal strategy for grid selection ish \leqslant O\left(\varepsilon^\beta / r\right), \tau \leqslant O\left(\varepsilon^\beta / 2\right). In addition, the Klein-Gordon equation with weak nonlinear term can be transformed into a form with high frequency oscillation by scaling in the time direction, that is, the solution changes gently in the spatial direction, but there is a high frequency oscillation with wavelength O(ε^β) in the temporal direction. The error upper bound and energy conservation properties of the scheme are verified by a large number of numerical results.