Due to carrier band-to-band tunneling (BTBT) through channel-source/drain contacts, traditional MOS(metal oxide semiconductor)-like carbon nanotube field effect transistors (CNFETs) suffer from quasi-ambipolar transport property, leaving much negative impacts on device performance and its application in circuits. To suppress such quasi-ambipolar behavior, a novel device design based on dual-gate-material device structure is proposed. The modeling results show that, with proper choice of tuning gate material, this device design can increase the ON-OFF current ratio by 6—9 orders of magnitude, tune the threshold region effectively and keep the sub-threshold slope immune from it. In addition, the quasi-ambipolar transport characteristic of C-CNFETs can be suppressed effectively using such novel device design. Further study reveals that the performance of the proposed design depends highly on the choice of tuning gate material, and the quantum capacitance in CNFETs has great effect on not only its subthreshold slope but also its transport polarity.