The growth of carbon nanotubes from catalytic thermal decomposition of acetylene on fine iron particles has been studied. Electron microscopic images of the carbon nanotubes "as formed" and after annealing treatment are presented. Besides the ordinary carbon nanotubes which have been reported (S. Iijima, Nature, 354 (1991) 56), we have found, at first time, two other new kinds of carbon nanotubes: one is straight or curved nanotube with many irregular multi-layered diaphragms in the hollow core, in particular, the fringes of the wa II of the tu bes a re not parallel to the axis of the tu be; another one has ma ny regular diaphragms (bamboo-like) which keep almost constant distance with each other. A model that postulates two steps growth of nanotubes from catalyst particles is proposed to explain the microstructure of the novel carbon nanotubes.