Carbon nanotubes (CNTs) have been under intense investigations during the past two decades due to their unique physical and chemical properties; however, there is still no commonly accepted growth mechanism to describe the growth behavior of CNTs. Here, we propose a nano Czochralski (CZ) model which regards the catalytic growth of a CNT as a CZ process taking place on the nano scale. The main idea is that, during the CNT growth, each catalyst particle acts as a nano crucible to nucleate and maintain the CNT growth, and the extruding CNT rotates relative to the nano crucible, leading to a chirality-dependent growth rate. In this case, the structural quality gradually changes along the CNT due to the dynamic generation-reconstruction-diffusion of defects during the CNT growth. The nano CZ mechanism may also apply to the catalytic growth of many other one-dimensional (1D) nanostructures (including various nanotubes and nanowires), thus further efforts will be stimulated in the quality and property control, as well as application explorations of these 1D nanomaterials.