The invention discloses a solar energy and fuel coal coupled flexible power generation system and a running method. The system comprises a coal-fired power generation unit thermodynamic system and a high-temperature heat storing system which comprises a solar heat collection system, cold and hot heat storing medium tanks, a heat storing medium pump, a heat storing medium and feed water heat exchanger and the like and is coupled with solar thermal power generation; a heat storing medium heater is arranged in a boiler flue; the flow of a heat storing medium entering the solar heat collection device and the heat storing medium heater is adjusted through cooperation of a solar heat storing medium adjusting valve and the heat storing medium pump, therefore, influences of sunlight irradiation changes are eliminated, and the output power is kept stable; peak regulation is conducted through the heat storing medium tank, and the steam turbine output power is reduced under the stable combustioncondition of a boiler; and the flow and temperature of feed water entering the heat storing medium and feed water heat exchanger are adjusted through opening and closing of a high-pressure heater adjusting valve group, and then the system meets the requirements of the quick load changing rate of a unit. According to the solar energy and fuel coal coupled flexible power generation system and the running method, solar energy and fuel coal power generation coupling can be achieved, coal consumption is reduced, and the flexibility and economical efficiency of the unit are significantly improved.