A boiler operating method operates a boiler by switching between air combustion mode and oxygen combustion mode when burning fossil fuel with first combustion gas and second combustion gas. The second combustion gas compensates for oxygen deficiency in the first combustion gas. The air combustion mode uses air as the first combustion gas and the second combustion gas while the oxygen combustion mode uses mixed gas of combustion flue gas and oxygen-rich gas as the first combustion gas and the second combustion gas, the combustion flue gas being produced when the fossil fuel is burned. By mixing the oxygen-rich gas in the air in the process of switching between air combustion mode and oxygen combustion mode, the air being the first combustion gas used in the air combustion mode, the boiler operating method can switch between the air combustion mode and oxygen combustion mode while maintaining stable combustion.