Theoretical calculations predict transition frequencies in the terahertz range for the field-effect transistors based on carbon nanotubes, and this shows their suitability for being used in high frequency applications. In this paper, we have designed a field-effect transistor based on carbon nanotube with high transition frequency suitable for ultra-wide band applications. We did this by optimizing nanotube diameter, gate insulator thickness and dielectric constant. As a result, we achieved the transition frequency about 7.45 THz. The environment of open source software FETToy is used to simulate the device. Also a suitable model for calculating the transition frequency is presented.