The present invention relates to a continuous method for functionalizing a carbon nanotube, and more specifically, to a continuous method for functionalizing a carbon nanotube by feeding functional compounds having one or more functional group into a functionalizing reactor into which a carbon nanotube mixture including oxidizer is fed under a pressure of 50 to 400 atm and a temperature of 100 to 600° C. to a subcritical water or supercritical water condition of a pressure of 50 to 40 atm by using a continuously functionalizing apparatus to obtain the functionalized products, such that the functional group of the functional compound can be easily introduced to the carbon nanotube, thereby increasing the functionalized effect of the carbon nanotube and increasing the dispersibility accordingly.