The mechanism of the carbon nanotube (CNT) formation and its graphitization has not been well understood and is still under controversy. The authors have been studying a new process to form CNTs, where polyyne-containing carbons are heated and irradiated by an electron beam in a transmission electron microscope (TEM). The technique is compatible to an in-situ observation and was applied to a high-resolution TEM (HRTEM) to elucidate the graphitization mechanism. The observation shows that micro-graphenes exist from the beginning of the formation process and develop to form highly ordered graphene layers through fusion and rearrangement of the premature layers, accompanied by evaporation of micro-graphenes. The CNT formation mechanism focusing on its graphitization is presented and discussed.