For the first time, in this paper a tunneling field effect transistor based on semiconductor carbon nanotubes with gate and drain overlap and dual material gate (OVDMG-T-CNTFET) is proposed and simulated using non-equilibrium Green's function (NEGF). This structure uses two metals with different workfunctions. The metal close to source has higher workfunction. This metal controls tunneling at source side of channel and increases ON state current. Drain side impurity penetrates to the channel region or in other words there is an overlap between drain and gate region. It is demonstrated that with proper selection of overlap length, the device static and dynamic behavior is enhanced. The conventional tunneling transistors suffer from low saturation current. The proposed structure considerably enhances the ON current which is important in sensing applications. Furthermore, this structure enhances current ratio, switching speed, unity-current-gain frequency f T , transconductance, subthreshold swing (SS), hot carrier effect, and drain induced barrier lowering (DIBL) in comparison with conventional structure.