Mixed lubrication is a major lubrication regime in the presence of surface roughness. A deterministic model is established to solve mixed lubricated point contact in this paper, using a new method to solve the asperity contact region in mixed lubrication. Treatment of pressure boundary conditions between elastohydrodynamic lubrication region and asperity contact region is discussed. The new model is capable of calculating the typical Stribeck curve and analyzing the transition of lubrication regime, from full film lubrication to boundary lubrication. Moreover, the final result of the model is independent of pressure initialization. High performance in accuracy and convergence has been achieved, which is of great importance for further lubrication modeling with consideration of nano-scale roughness, intermolecular, and surface forces.