The invention discloses a catalyst for synthesizing a carbon nanotube, and the catalyst includes a support containing a metal, and an active metal impregnated on the support. The active metal includescobalt and manganese. A surface molar ratio of the active metal relative to the metal of the support is 40% or less of a bulk molar ratio of the active metal relative to the metal of the support. A carbon nanotube having high purity and low resistance is obtained from the catalyst.