The effect of quantum capacitance (QC) on the switching speed in T-CNFETs (Tunneling Carbon Nanotube Field Effect Transistors) is investigated with simulation using NEGF (Non-Equilibrium Green's Function) formalism. Firstly, based on the analytical expression of SS, a quantitative study of the source/drain leads doping level is made to obtain an averaged inverse subthreshold slope(SS) as small as possible. And then the impact of QC on the gate control, thus on SS, is studied. Lastly, for the first time, approaches for restricting the impacts of QC are investigated, such as tuning the drain-source bias condition or CNT diameter which are governed by the analytical expression presented at the end of this paper. The modeling results reveal that the QC in T-CNFET has a negative impact on both the SS and on-current, and such impact could be restricted effectively with a proper choice of drain-source voltage and CNT chirality.