The process of making carbon nanotube array includes the following steps: providing one substrate and forming one mask layer on the substrate; providing one catalyst source and sputtering catalyst layer of certain thickness gradient and with some point in optimal thickness on the substrate with mask; eliminating the mask and annealing the catalyst layer; introducing carbon source gas to grow carbon nanotube array bending opposite to the point in optimal thickness. The present invention realizes the local control of carbon nanotube array growth.