A method for forming a carbon nanotube array includes the following steps: providing a smooth substrate (11); depositing a metal catalyst layer (21) on a surface of the substrate; heating the treated substrate to a predetermined temperature in flowing protective gas; and introducing a mixture of carbon source gas and protective gas for 5-30 minutes, thus forming a carbon nanotube array (61) extending from the substrate. When the mixture of carbon source gas and protective gas is introduced, a temperature differential greater than 50° C. between the catalyst and its surrounding environment is created by adjusting a flow rate of the carbon source gas. Further, a partial pressure of the carbon source gas is maintained lower than 20%, by adjusting a ratio of the flow rates of the carbon source gas and the protective gas. The carbon nanotubes formed in the carbon nanotube array are well bundled.