The growing problem of global warming in the refrigeration industry requires the replacement of existing refrigerants and further enhancement of heat transfer efficiency in heat exchangers. The boiling heat transfer characteristics of R513A in the horizontal smooth tubes and internally ribbed tubes with outer diameter 9.52, 12.70 mm were experimentally investigated to analyze the mechanism of changes in heat transfer coefficients and pressure drops by heat flux, tube diameter, mass flux and saturation temperature. The results show that the boiling heat transfer coefficient increases and then decreases with the increase of heat flux. The disturbance of refrigerant in the 9.52 mm smooth tube is more intense, and the heat transfer coefficient is increased by 13.91%～19.77% compared with that of the 12.70 mm tubes. The pressure drop in the 9.52 mm tubes is 1.4～3.8 times that of the 12.70 mm tubes. Both the increase in saturation temperature and the increase in mass flux contribute to the heat transfer coefficient. It is easier to reach the local drying point at low mass fluxes, when the boiling heat transfer coefficient decreases sharply. The Cooper and Liu-Winterton correlations were compared to predict the heat transfer coefficients. Before the drying out, both of them can predict the flow boiling heat transfer characteristics of R513A in the horizontal smooth tube very well. After the drying out, the Liu-Winterton correlation is more accurate, with mean absolute deviation of 18.53% and 28.36% before and after the drying out, respectively.