<p>Air source heat pump has insufficient heating performance under the low ambient temperature conditions; meanwhile, the thermal storage device in heat pump system has a wide range of application. This study proposes a thermal storage air source heat pump heating system (HSASHP) with a novel structure, and has established both the mathematical models and simulation models of each component of the single-stage and the thermal storage air source heat pump heating systems in MATLAB/Simulink respectively, with three operation modes proposed for the latter (i.e., the thermal storage air source heat pump heating system); by using the outdoor ambient temperature during the heating period in Baotou, China, the heating capacity of the two heat pump systems are simulated and the economy of both systems’ operation are investigated. The results show that within a 7-day heating period, the total heat production of the thermal storage heat pump unit and the single-stage heat pump unit is 442.58 kW·h and 355.68 kW·h, respectively, with HSASHP 24% higher; the average heating Coefficient of Performance (COP) of the two heat pump units is 2.11 and 1.51, respectively, with HSASHP 39.74% higher; the power consumption of the two heat pump units is 202.74 kW·h and 239.74 kW·h, respectively, with HSASHP 15.44% lower. These all illustrate the effectiveness of the new structure in improving the performance of heat pump units. However, the total power consumption and operational economy of both air source heat pump heating systems do not differ significantly.</p>