Influence of hydrocarbon partial pressure on single carbon nanotube (CNT) growth in chemical vapor deposition is investigated by a new theoretical model based on kinetic theory of gases and, phonon vibrations of carbon nanotube on catalyst. Results show that CNTs with larger diameter grow lesser owing to higher damping factors and CNT inertia. In addition, an optimum temperature for the growth is obtained for a CNT with a specific diameter and catalyst. Also it is shown that the optimum temperature is changed by using different catalysts. Finally effect of the partial pressure on the growth is also discussed. It is demonstrated that increasing partial pressure leads to the longest CNTs and also, influence of partial pressure on CNTs with smaller diameters is stronger All results of the presented mechanism are in good agreement with reported experimental results. (C) 2014 Elsevier B.V. All rights reserved.