Heating capacity of an air-source heat pump (ASHP) system often decreases when it is operated in winter. This is because of frosting significantly affects the heat transfer efficiency of evaporator, and thus the airflow passage blocked. In order to solve this problem, a novel frost-free ASHP system, integrated with dehumidification and thermal energy storage, has been developed. In this paper, to further investigate the dynamic characteristics of the system working at low temperature, a mathematical model of the novel frost-free ASHP system was constructed. The mathematical model was verified by comparison with experimental data that showed that the measured results were in good accordance with the numerical ones. According to the mathematical model, the research results indicated that, at relatively humidity (RH) of 80%, the system average COP increased by 56.2% when ambient temperature increased from −10 °C to 0 °C. However, it decreased by 6.7% when RH increased from 75% to 85% at temperature of 0 °C. In addition, the system average COP at the air velocity of 3.0 m s−1 was higher 0.22 and 0.16 than that of 2.5 m s−1 and 3.5 m s−1. Finally, the correlations of the system frost-free working time and the system COP with ambient temperature and relative humidity were obtained, respectively, by multivariate linear regression. These results provided a basis in improving and optimizing the thermal system COP and other main performance parameters.