A method of growing carbon nanotubes is related. A reactor is provided. The reactor includes a reactor chamber and a carbon nanotube catalyst composite layer suspended in the reactor chamber. The carbon nanotube catalyst composite layer includes a carbon nanotube layer and a number of catalyst particles dispersed in the carbon nanotube layer. A mixture of carbon source gas and carrier gas is introduced into the reactor chamber to penetrate the carbon nanotube catalyst composite layer. The carbon nanotube catalyst composite layer is heated.