The phenomenon of coherence resonance in a nonlinear integrate-and-fire neuronal model subject to correlated multiplicative synaptic and additive voltage-gated channel noise are investigated. Based on the adiabatic approximation theory and the unified colored approximation method，the analytic expression of the probability distribution of the first fire （FPD） and the coefficient of variation （CV） of the inter-spike interval of firing are obtained. It is shown that the FPD and the CV are functions of the intensity of the multiplication synaptic colored noise，the additive voltage-gated channel white noise，the correlation time of multiplicative noise and the strength of the correlation between noises. By choosing appropriate noise parameters，the phenomenon of coherence resonance can occur. Meanwhile，the effects of intensity of the multiplication synaptic noise，the additive voltage-gated channel noise，the correlation time of multiplicative noise and the strength of the correlation between noises on coherence resonance are discussed.