An R-cut substrate is prepared by cutting from Lumbered synthetic quartz crystal in a plane parallel to the R plane. The R plane, which is the smoothest plane in crystal structure, accounts for most of the surface of the R-cut substrate obtained as above, and the m-plane and the r-plane lightly appear in the surface of the R-cut substrate in directions parallel to the X-axis during processing. After placing catalyst metal on the surface of the R-cut substrate, carbon containing gas is supplied to the surface of the R-cut substrate, and carbon nanotubes are grown along the lattice structure of the crystal using the catalyst metal as a core. With this, carbon nanotubes having excellent orientation and linearity can be manufactured.