The invention discloses a fine particulate matter removing device with a Sierpinski sponge structure in the technical field of environmental protection. A Sierpinski sponge model structure is applied to particulate removal, and thus a novel industrial dust removing device is formed; a spraying member is fixed above the outlet section of a Sierpinski sponge structure passage through a support frame; a water supply pipeline communicated with the spraying member is arranged in the center of the spraying member; the spraying member is periodically opened and closed to periodically clean fine particulate matters in the passage, so that the passage is kept clean; and high-temperature flue gas is used as a heat source and flows in from the passage inlet of the sponge structure, the flue gas and the surface of the Sierpinski sponge model structure passage form a temperature field, and the fine particulate matters in the flue gas can be effectively removed by using thermophoresis deposition effect and turbulence effect. The removing device can be arranged on a particulate exhaust system such as a flue gas system of an industrial boiler, an exhaust chimney of a nuclear power station or an automotive exhaust system, is safe, efficient, reliable, convenient to implement and easy to control, and can realize modularized assembly.