Amorphous carbon films have attracted much attention in the field of abnormal discharge of vacuum microwave devices and equipment due to their extremely low secondary electron yields (SEYs). However, the dynamic process and microscopic mechanism of the effect of amorphous carbon film on secondary electron emission are still poorly understood. In this work, a numerical simulation model of the secondary electron emission of amorphous carbon film on copper surface is developed by the Monte Carlo method, which can accurately simulate the dynamic processes of electron scattering and emission of the film and the substrate. The results show that the maximum SEY decreases by about 20% when the film thickness increases from 0 to 1.5 nm. Further increasing the thickness, the SEY no longer decreases. However, when the film is thicker than 0.9 nm, the SEY curve exhibits a double-hump form, but with the thickness increasing to 3 nm, the second peak gradually weakens or even disappears. The electron scattering trajectories and energy distribution of secondary electrons indicate that this double-hump phenomenon is caused by electron scattering in two different materials. Compared with previous models, the proposed model takes into account the change of work function and the effect of interfacial barrier on electron scattering path. Our model can explain the formation of the double-hump of SEY curve and provides theoretical predictions for suppressing the SEY by amorphous carbon film.