A charge multiplication model of charge carrier multiplier (CCM) in electron-multiplication charge-couple-device (EMCCD) was proposed. The EMCCD architecture and the theory of CCM with its performance on electrons multiplication were analyzed. The transform function of charge multiplication in CCM was presented based on Z transform, as well as the amplitude-frequency response. The results show that amplitude-frequency response of CCM increases as the charge multiplication ratio increases. Then gain-fluctuation was studied with the gain-fluctuation factor, and the relation between gain-fluctuation factor, charge multiplication ratio α and CCM stages N was obtained. The numerical results show that the gain-fluctuation factor increases as α increases for α≤0.15 and N=400, but the gain-fluctuation factor decreases as α increases for α≥0.15. Those numerical results are validated with practical experience.