A source-overlapped dual-material gate TFET (SODM-TFET), which features different materials in its source-overlapped and channel gates, is proposed here, and its performance is investigated for various channel and source gate work functions (ψmc and ψms, respectively). Previous studies reported a hump effect in source-overlapped TFETs (SO-TFETs) and relatively high currents in the ambipolar state. The flat-band voltage in our SODM-TFET was controlled by modulating ψms and ψmc, allowing to reduce the hump effect and suppressing the ambipolar current. Compared with conventional SO-TFETs, minimal subthreshold-swing (SSmin) and average SS (SSavg) of our SODM-TFET were ~4 and ~3.5 times lower, respectively. The on/off current ratio (Ion/Ioff) of the SODM-TFET increased by ~100, while the on-current (Ion) of the SODM-TFET increased by ~100 at the supply voltage of 0.7 V.