As a renewable energy power generation method, concentrating solar power generation has a broad application prospect. Weather and fluctuation significantly affect the output power of concentrating solar power generation. A heat storage system can stabilize this fluctuation and generate continuous and stable power. Therefore, the research on heat storage systems is of great significance to the development of concentrating solar power generation. This paper mainly studies the operating characteristics of the heat storage system based on solar energy in simultaneous charging, the influence in the change in solar radiation intensity on the charging power and the discharging outlet temperature, and the feasibility of the heat storage tank as an inertial link to stabilize the fluctuation in solar energy and the discharging outlet temperature. In this study, an experimental system for heat storage was established, in which solar energy was used as the heat source, water was used as the heat transfer fluid, and paraffin was used as the phase change heat storage material. When the initial temperature is 50 °C and the charging flow rate is maintained at 0.7 m3/h, at the same time the discharging flow rate is 0.1 m3/h, 0.3 m3/h, and 0.5 m3/h, respectively. The results show that when the solar radiation intensity is lower than 548 W/m2, the curve of heat storage power is almost parallel to the curve of solar radiation intensity; when the solar radiation intensity is lower than 535 W/m2, the moving direction of the thermocline will change; the average discharging outlet temperature in each case is higher than the phase change temperature of the phase change material and this system can continuously supply hot water at more than 69 °C for more than 3 h 32 min; and increasing the discharging flow rate will increase the whole charging and discharging time, thicken the thermocline, and disturb the temperature field in the tank. The experimental analysis will be conducive to profoundly understanding the operation characteristics of the thermocline heat storage tank under the solar heat source and has reference value for the subsequent design of a more efficient heat storage system.