A dynamic friction coefficient model in engagement was established based on the friction transmission mechanism of a wet clutch. The effects of parameters, such as the material permeability, surface roughness, Young’s modulus, ATF viscosity, applied pressure, initial relative angular velocity, and pressure delay time, on the friction coefficient during engagement were investigated. The results indicated that material permeability has a greater influence on the time when the dynamic friction coefficient tends to be stable, choosing an appropriate permeability of friction material can effectively prevent excessive the level of jerk during the engagement and excessive engagement time. Surface roughness and applied pressure mainly affect the magnitude of the initial and midpoint friction coefficients. Appropriately increasing the surface roughness and applied pressure can increase the smoothness of the engagement of wet clutch. The ATF viscosity and initial relative angular velocity have a significant effect on the magnitude of the initial friction coefficients. Appropriately increasing the ATF viscosity and initial relative angular velocity will reduce the level of jerk at the end of the wet clutch engagement. Young’s modulus and the pressure delay time have a smaller effect on the dynamic friction coefficient than that of other parameters.