Carbon nanotube field-effect transistors (CNTFETs) with a cylindrical surrounding gate and Schottky-barrier contacts to the source and drain are investigated by solving the self-consistent two-dimensional Poisson equation with the non-equilibrium Green's function equations. A simple effective-mass approach has been taken to deal with the transport problem in the CNTFETs, which, nonetheless, yields device characteristics that are in good agreement with those obtained by using more complex atomistic simulations. The low on/off current ratios due to the presence of both electron and hole conductions in the off-state region are improved by separately controlling the carrier injections at the source and drain contacts: CNTFETs with the CNT channel partially gated toward the source and those with the CNT channel partially n-doped toward the drain have been considered, and improvements in the on/off ratios of up to five orders of magnitude have been obtained.