A vertical carbon nanotube field-effect transistor (CNTFET) based on silicon (Si) substrate has been proposed and simulated using a semi-classical theory. A single-walled carbon nanotube (SWNT) and an n-type Si nanowire in series construct the channel of the transistor. The CNTFET presents ambipolar characteristics at positive drain voltage (Vd) and n-type characteristics at negative Vd. The current is significantly influenced by the doping level of n-Si and the SWNT band gap. The n-branch current of the ambipolar characteristics increases with increasing doping level of the n-Si while the p-branch current decreases. The SWNT band gap has the same influence on the p-branch current at a positive Vd and n-type characteristics at negative Vd. The lower the SWNT band gap, the higher the current. However, it has no impact on the n-branch current in the ambipolar characteristics. Thick oxide is found to significantly degrade the current and the subthreshold slope of the CNTFETs.