We have investigated the thermal rectification phenomenon in a single-wall mass graded carbon nanotube by molecular dynamics simulation. Second generation Brenner potential has been used to model the inter atomic carbon interaction. Fixed boundary condition has been taken into account. We compare our findings to a previous study by Alaghemandi et al.  which has been done with a different potential and boundary condition. The dependence of the rectification factor R on temperature, nanotube diameter and length as well as mass gradient is obtained. It is shown that by increasing the temperature, the rectification decreases whereas by increasing the other parameters namely the mass gradient, diameter and the tube length it increases.