Fine catalyst particles are loaded on a sol-gel method porous carrier having fine pores of 0.1-50 nm and a carbon compound is decomposed to form a carbon nanotube film on the carrier that is aligned perpendicular to the carrier surface. The starting sol to be processed by a sol-gel method is a dispersion of fine alumina particles, fine aluminum hydroxide particles, fine silica particles or mixtures thereof. Alternatively, the starting sol may be an aluminum alkoxide, an alkoxysilane, a mixture thereof or a solution of an aluminum alkoxide, an alkoxysilane or a mixture thereof. If desired, a flammable or a thermally decomposable organic compound may be added as a microporous template.