A device for effectively removing organic compounds from air by a carbon nanotube-catalyst composite having the two functions of an adsorption/catalytic incineration agent is provided. The carbon nanotube-catalyst composite simultaneously adsorbs the organic compounds and completely decomposes them by a catalytic reaction, and the optimal reaction active temperature by catalytic incineration is low. The carbon nanotube-catalyst composite has a large surface area and has high adsorption performance and catalytic decomposition activity, and is thus applicable to filters that use the methods of adsorption and/or catalytic incineration. The device for removing organic compounds from air includes an adsorption/catalytic incineration reactor including the carbon nanotube-catalyst composite to remove organic compounds from air.