To prevent dioxins in dust being gathered inside a duct or the like when a high-temperature exhaust gas flows from being scattered again after a low- temperature exhaust gas flows.

Two groups of systems for treating a high-temperature gas being generated from an electric furnace 1 for steel manufacture are provided. When the temperature of the exhaust gas is equal to or more than a fixed value being predetermined based on the combustion decomposition temperature of dioxin, the exhaust gas is cooled by a cooling device 10 and is purified and treated by a dust collector 12. When the temperature of the exhaust gas is less than the fixed value, the exhaust gas is led to and is cooled by another cooling device 10' and is purified and treated by a dust collector 12' at the downstream of the cooling device 10'. In this case, the fixed temperature is 800°C, thus satisfying the target value (for example, 0.5 ng-TEQ/ Nm3 or less) of the concentration of dioxins in the exhaust gas being dissipated into air, at the same time, reducing the absolute value of exhaustion and the amount of the treatment of the dust containing dioxins, and, furthermore, eliminating the need for secondary burning facilities as in a conventional combustion decomposition method and the running costs.