There is provided a method of purifying single wall carbon nanotubes so as to be able to remove impurities such as a metal catalyst to obtain the single wall carbon nanotubes with high purity. The method includes the first oxidizing step of oxidizing the single wall carbon nanotubes soot 1 containing an impurity with a metal catalyst 2, the first refluxing step of refluxing the single wall carbon nanotubes soot 1 obtained by the first oxidizing step in an acid solution, the second oxidizing step of oxidizing the single wall carbon nanotubes soot 1 obtained by the first refluxing step, and the second refluxing step of refluxing the single wall carbon nanotubes obtained soot 1 by the second oxidizing step in an acid solution. The single wall nanotubes 1 are synthesized by an arc discharge with a carbon electrode containing a metal catalyst 2. The carbon electrode contains a metal catalyst which consists of Ni, Y, and Ti. The first oxidizing step is performed by heating at a temperature between 350 and 600.degree. C. or by a wet-oxidization in hydrogen peroxide solution. The first refluxing step is performed by refluxing in nitric acid. The second oxidizing step is performed by wet-oxidizing in hydrogen peroxide. The second refluxing step is performed by refluxing in hydrochloric acid.