A coupled mathematical model on moment, energy and mass transport is developed to investigate fluid flow, heat transfer, solidification, solute transfer and inclusion collision-growth in the continuous casting mold. Numerical results show that the temperature of molten steel, carbon and inclusion in the molten steel have the similar spatial distribution as the fluid flow in the continuous caster due to the flow behavior of molten steel. Their spatial distribution can be divided into the upper and lower recirculation zones. But their distributions have their own characteristics. Near the center of the recirculation zones, the temperature of molten steel is lower, the carbon concentration is higher and the volume concentration and number density of inclusion is lower. Near the meniscus, the temperature and the volume concentration and number density of inclusion is lower, and the carbon concentration is higher. Because the solidified shell is re-melted near the impinging point, there is the abrupt transition for inclusion concentration and number density distribution in the solidified shell at the mold exit.