Current transport in carbon nanotube field effect transistors (CNT-FETs) has been modeled from charge distributions and the potential inside the carbon nanotube. Analytical equations describing I-V characteristics of the CNT-FETs have been obtained from the combination of diffusion and drift mechanisms in the channel region for normal and sub-threshold operations. It is shown that the electronic transport in semiconducting single-walled carbon nanotubes and field effect transistors can provide better understanding of their bio- and chemical sensing for the detection of traces of agents at molecular levels.