A CNT composite (10) includes a matrix (14) and a number of CNTs (12) embedded in the matrix. The matrix has a surface (102) and an opposite surface (104). Head portions of the respective CNTs are consistently oriented, parallel to the surfaces of the matrix. A method for manufacturing the composite includes (a) providing a substrate and depositing a catalyst film on the substrate; (b) forming the array of CNTs via the catalyst film on the substrate; (c) immersing the CNTs in a liquid matrix material, infusing the liquid matrix material into the array of CNTs; (d) taking the carbon nanotubes with the infused matrix out of the liquid matrix; (e) pressing the still-soft matrix and the CNTs therein, in order to arrange the CNTs consistently and parallel to the surfaces of the matrix; and (f) solidifying and peeling away the matrix to produce the CNT composite.