The present invention relates to a continuous method and apparatus of functionalizing a carbon nanotube, and more specifically, to a continuous method of functionalizing a carbon nanotube under subcritical water or supercritical water conditions without additional functionalizing processes, comprising: a) continuously feeding the carbon nanotube solution and an oxidizer under a pressure of 50 to 400 atm, respectively or together, and then preheating the mixture of said carbon nanotube solution and said oxidizer; b) functionalizing the carbon nanotube in the preheated said mixture under the subcritical water or the supercritical water condition of 50 to 400 atm; c) cooling down the functionalized product into 0 to 100° C. and depressurizing the functionalized product into 1 to 10 atm; and d) recovering the cooled down and depressurized product.