This paper deals with a prediction method for the condensation of ternary refrigerant mixture inside a horizontal smooth tube. Based on some reliable assumptions, the governing equations for the local heat and mass transfer characteristics are derived, and the prediction for the condensation of ternary zeotropic refrigerant mixtures composed of HFC32/HFC125/HFC134a, including R407C, is carried out. The local values of vapor quality, thermodynamic states at bulk vapor, vapor-liquid interface and bulk liquid, mass flux etc. are obtained for a constant wall temperature and a constant wall heat flux conditions, and the effects of the composition of HFC32/HFC125/HFC134a on heat transfer characteristics are examined. The prediction result is also compared with experimental data for condensation of ternary refrigerant mixtures. The predicted wall temperature distribution has a similar trend with experimental data but the predicted local heat transfer coefficients are 20-30% higher than the experimental data.