Disclosed is a method for manufacturing an iron catalyst, the method including: a mixing stage where a mixture solution is manufactured by mixing iron nitrate (Fe(NO3)3) solution and copper nitrate (Cu(NO3)2) solution; a precipitation slurry-forming stage where a precipitation slurry is formed by adding at least one of sodium carbonate (Na2CO3) or sodium hydroxide (Na2CO3) solutions to the mixture solution; a washing stage where the precipitation slurry is filtered and washed with distilled water; a silica adding stage where fumed silica powder and potassium carbonate (K2CO3) solution are added to the precipitation slurry and then agitated; a drying stage where the precipitation slurry is passed through a sieve having a size of 30 μm to 100 μm and dried by a spry drying method to manufacture a powdered iron catalyst; and a heat treatment stage where the iron catalyst is dried at a temperature of 50° to 150° C., and then heat-treated at a temperature of 300° C. to 500° C.