A flue-gas purification system includes a flue-gas cycling system, a reactor, an absorbent adding system having at least a catalytic absorbent, wherein the catalytic absorbent is being gasified for reacting with the flue-gas in the reactor in a homogenous gas-gas phase reacting manner. Therefore, the purification system has fast reaction rate between the pollutants of the flue-gas and the catalytic absorbent, which is preferably ammonia, to efficiently remove pollutants, so as to effectively purify the flue-gas.