In this paper, we propose and evaluate a novel design of a lightly doped drain and source carbon nanotube field effect transistor (LDDS-CNTFET) with a negative differential resistance (NDR) characteristic, called negative differential resistance LDDS-CNTFET (NDR-LDDS-CNTFET). The device was simulated by using a non equilibrium Green’s function method. To achieve this phenomenon, we have created two quantum wells in the intrinsic channel by using two n-type regions. In the wells that are separated by a thin barrier, two resonance states are generated. On the other hand, the thickness of the barrier between the source and the well is variable depending on the energy level. Accordingly, with increasing gate-source voltage, the number of tunneling electrons and consequently drain-source current are varied. Furthermore, we have presented a structure with two n-type and three p-type regions in the channel that illustrates a larger NDR region. In this structure, the peak and valley of the drain-source current are shifted when compared with the previous structure. Finally, we investigated the effect of doping concentration on the NDR parameter.