The invention discloses a method and a system for removing mercury through free radicals generated based on ozone/hydrogen peroxide. The method comprises the following steps that smoke exhausted by a combustor firstly passes through a smoke heat exchanger to be adjusted in temperature and then is introduced into a liquid phase reaction region of a reactor; ozone is injected into the smoke at a reactor inlet flue by an ozone injector; the ozone in the smoke contacts with hydrogen peroxide in a solution in a liquid phase reaction region to generate hydroxyl radicals to oxidize and remove an elementary substance mercury in the smoke, wherein a reactant is divalent mercury easily dissolving in water; after entering a primary mercury separation tower, a reaction solution generates a mercuric sulfide precipitate through reaction by adding sulfide and then is kept to be introduced into a secondary mercury separation tower for precipitation and separation. The method is capable of efficiently removing the elementary mercury in the smoke; equipment is simple and reliable, and free from secondary pollution in a removing process, thus the method and the system are novel smoke purifying method and system with wide application prospect.