The present invention relates to a composite material of carbon nanotubes and the manufacture method. The composite material of carbon nanotubes comprises a matrix and a plurality of carbon nanotubesdistributed in the matrix. The carbon nanotubes are arranged along the same direction parallel to the matrix surface in the matrix and the ends of the upward adjacent carbon nanotubes along the arranging direction are close to or contact each other. The manufacture method of the carbon nanotubes contains the following steps: (1) a stripped activator is made at an underlay surface. (2) The carbon nanotubes arranged directionally grows in the activator. (3) The carbon nanotubes are immersed into the matrix material, to which a firming agent is added. (4) When the matrix material is not solidified completely, the carbon nanotubes are pressed down by a tool, which makes the carbon nanotubes to be arranged transversely along the same direction in the matrix. (5) When matrix material is solidified completely, the composite is peeled off from the underlay to form the composite material of carbon nanotubes.