This paper develops a generalized 3-dimensional 14-DOF dynamic model for hypoid gear which considers the time-varying friction coefficient and lubrication situation. We propose a mixed elastohydrodynamic lubrication(EHL) friction model of hypoid gear tooth contact to reflect the realistic lubricant situation in gear transmission system consisted of full film contact and asperity contact. Under the mixed lubrication condition, the effects of time-varying friction coefficient on gear dynamic is analyzed. The load sharing coefficient is used to calculate the instantaneous friction coefficient at each contact point along the contact path. Friction coefficient model based on mixed elastohydrodynamic lubrication(Mixed EHL) is incorporated into the dynamic model to predict the dynamic mesh force and transmission error with constant and time-varying friction coefficient. The simulation results under a wide range of speed and load show that the time-varying friction coefficient has a marginal effect on the dynamic response.