Provided is a continuous method and apparatus for purifying carbon nanotubes. Carbon nanotube is fed together with solvent into a preheater via a heat exchanger to produce a carbon nanotube mixture. The carbon nanotube mixture is preheated at 100 to 370° C. Then, the carbon nanotube mixture is purified in a purifying reactor under a subcritical water condition of 50 to 400 atm. The resulting purified product is cooled down to 0 to 100° C. and depressurized into 1 to 10 atm by feeding the purified product into a cooling down and depressurizing part via the heat exchanger. Finally, the cooled and depressurized product is recovered.