In this paper, a simulation model of a photovoltaic-air-source heat pump heating system with thermal energy storage (TES-PV-ASHP) is established using TRNSYS software, and a hot water storage tank is employed as the thermal energy storage device. An independent single-story building in Yan’an is selected as a research case to analyse the indoor heating load demand in the heating season. Considering the local solar energy resource characteristics and time-of-use electricity prices, a system operation strategy utilizing the water tank for energy storage is proposed, which achieves energy storage and allocation by adjusting the water tank temperature during periods of excess photovoltaic power and off-peak electricity price periods. An optimization model for water tank temperature settings is constructed based on the non-dominated sorting genetic algorithm Ⅱ (NSGA-Ⅱ). The results show that compared with the benchmark system operation strategy with a constant water tank temperature setting, the proposed system operation strategy increases the system revenue by 7.98%, enhances the photovoltaic self-consumption by 24.13%, and reduces the electricity consumption from the grid during peak electricity price periods by 40.82%.