A semiclassical method is used to simulate the characteristics of vertical carbon nanotube fieldeffect transistors on p-GaAs. The calculation results show unique transfer characteristics that depend on the sign of the drain voltage. The transistors exhibit p-type characteristics and ambipolar characteristics for a positive drain voltage and a negative drain voltage, respectively. The p-type characteristics do not change with the GaAs bandgap and doping level, because the hole current from the single-walled carbon nanotube (SWCNT) and drain side dominates the whole current. In contrast, the ambipolar characteristics are greatly influenced by the GaAs bandgap and doping level. Only the electron current in the ambipolar characteristics increases as the GaAs bandgap decreases. Increasing the p-type doping of GaAs increases the p-branch current and decreases the electron current (n-branch) of the ambipolar characteristics. The effects of the SWCNT bandgap and doping level are different from those of GaAs, and the impact of SWCNT on the p-type characteristics is much greater than the impact on the ambipolar characteristics. The p-type current increases as the SWCNT bandgap decreases.