Abstract: A new numerical scheme for the multi-symplectic complex modified KdV equation is constructed by the second order average vector field method and pseudo-spectral method. The corresponding discrete global energy conservation property of the new schemes is proved. The new schemes are applied to simulate the solitary wave evolution behaviors of the complex modified KdV equation with different initial conditions. The preserving energy conservation property is analyzed. Numerical results show that the new schemecan preserve the discrete global energy conservation property.