Carbon nanotubes are known as an interesting material to be used in the next generations of electronic technology, especially at nano regime. Nowadays, carbon nanotube field effect transistor or CNTFET is one of the promising devices for future electronic applications. A CNTFET which uses carbon nanotube as channel or source/drain region is the most promising candidate for replacing the current silicon transistor technology. The study of modern manufacturing approach and impact of device parameters on its performance is one of the important research fields in nanoelectronics. In this paper we study some aspects of changes in gate parameters at different channel diameters. This paper shows that for small values of diameter, increasing the dielectric constant of gate insulator doesn't help to improve the performance as value of dielectric constant of gate insulator reaches a certain amount. Also, increasing the oxide thickness of gate insulator doesn't always decrease transistor performance. For high diameter values, increasing the thickness up to a certain value improves the transistor performance.