For carbon nanotubes with open end, the relation between the distribution of frontier orbitals and the edge structure was studied by the Huckel and ab initio molecular orbital methods. When the edge of a nanotube takes a zigzag form, the frontier orbitals localize at the edge part irrespective of the tube length, and continuous growth can be expected according to the frontier electron theory; when the edge takes an armchair form, the frontier orbitals delocalize all over the tube surface, disfavoring the nanotube growth. These results coincide with the experimental observation by Sattler et al.