Revealing a "true" picture of the carbon nanotube (CNT) growth front at the catalyst surface is critical to understanding the mechanism of CNT growth. If the CNT-catalyst interface is clean or messy, which will greatly affect the mechanism of controlled CNT growth, has never been properly solved either experimentally or theoretically. Here, this issue by ab initial calculation-based kinetic analysis and classical molecular dynamic (MD) simulations is revisited. It is found that the appearance of carbon chains at the CNT-catalyst interfaces or the "messy" interfaces in MD simulations is a consequence of the very short simulation time, and a "clean" CNT-catalyst interface will emerge if the simulation time is close to that in real experiments. This study reveals that, during real CNT experimental growth, a "clean" CNT-catalyst interface with zigzag, armchair, and/or kink sites dominates the growth kinetics, and therefore, the controllable CNT growth by tuning the CNT-catalyst interface is feasible.