Carbon nanotubes (CNTs) have attracted much attention for their unique properties, although their formation mechanism is not well understood. The authors have been studying a technique to form CNTs by an electron beam that is carried out in a transmission electron microscope (TEM) and is compatible with in situ and real-time observation of the growth. The observation, where a precursor (polyyne-containing carbon) is heated and irradiated by an electron beam, shows that the growth occurs in two steps: rapid formation of rodlike carbon (first step) and slow graphitization of its wall (second step). The hollow inside the CNT is not formed in the first step and develops during the second. The formation mechanism is discussed in relation to in situ observations.