In this paper a heterostructure tunneling carbon nanotube field-effect transistor, namely H-T-CNTFET, is introduced. In the proposed structure, a carbon nanotube with a different chirality is used for the drain side compared to the source and the channel region. Characteristics of the proposed structure are numerically simulated by a mode-space non-equilibrium Green's function formulism in the ballistic limit. Simulation results show that, compared to a conventional tunneling carbon nanotube field-effect transistor, the proposed structure has higher ON-current, better ambipolar behavior and better switching characteristics. In addition, the analog characteristics of the device, such as the transconductance (g(m)) and unity-gain frequency (f(T)), are also improved.