Abstract: Carbon Nanotube is one of the rising technologies within nano science, which is showing high efficiency and wide range of applications in many different fields of science and technology. The Carbon Nanotube Field Effect Transistors (CNTFETs) have been explored and proposed to be the rising candidate for the next generation of integrated circuit (NGIC) devices. In this paper first the Carbon Nanotube and density of state (DOS) with different types of nanotubes considering energy gap have been reviewed. We have then studied the carbon nanotube field effect transistor. In this research CNTFET is analyzed where the bandgap is 0.94eV with HfO2 as gate dielectric. Finally the simulation of proposed model is given.