The invention discloses a sulfur recovery device and method applicable to high operating flexibility.According to the device, a pipeline (1) and a pipeline (2) are arranged on the top of a heat recovery boiler to be connected with a low-pressure saturated steam header pipe and a medium-pressure saturated steam header pipe respectively, and the pipeline (1) and the pipeline (2) are each provided with a pressure control valve; a low-temperature outlet of the heat recovery boiler is connected with an inlet of a first-stage sulfur condensation cooler, and an outlet of the first-stage sulfur condensation cooler is connected with a regulating valve through a pipeline (3); a high-temperature mixture valve is arranged at a high-temperature outlet of the heat recovery boiler, an inlet of the high-temperature mixture valve is connected with the regulating valve, and an outlet of the high-temperature mixture valve is connected with an inlet of a first-stage Klaus reactor through a pipeline (4).According to the sulfur recovery device and method applicable to the high operating flexibility, the operating flexibility, ranging from 30% to 120%, of a traditional sulfur recovery device can be effectively improved to 10%-120%, so that the large-load-change resistant capacity of upstream and downstream devices of a refinery plant and the sulfur recovery device is higher, and it is guaranteed that the plant operates continuously and stably in a long period.