Carbon nanotubes are directly grown on a substrate surface having three metal layers thereon by a thermal chemical vapor deposition at low-temperature, which can be used as an electron emission source for field emission displays. The three layers include a layer of an active metal catalyst sandwiched between a thick metal support layer formed on the substrate and a bonding metal layer. The active metal catalyst is iron, cobalt, nickel or an alloy thereof; the metal support and the bonding metal independently are Au, Ag, Cu, Pd, Pt or an alloy thereof; and they can be formed by sputtering, chemical vapor deposition, physical vapor deposition, screen printing or electroplating.