The growth of single-wall carbon nanotube from graphite layers is studied by tight binding molecular dynamics simulation. Given temperature of 2500 K or 3500 K and an interval of 0.25 nm for the two layers of graphite, a single-wall carbon nanotube with a zigzag shell will be produced. On the other conditions the carbon nanotube cannot grow or grows with too many defects. All carbon nanotube ends have pentagons which play an important role during the tube ends closing.