A III-V heterojunction tunneling field-effect transistor (TFET) can enhance the on-state current effectively, and GaAs x Sb 1−x /In y Ga 1−y As heterojunction exhibits better performance with the adjustable band alignment by modulating the alloy composition. In this paper, the performance of the cylindrical surrounding-gate GaAs x Sb 1−x /In y Ga 1−y As heterojunction TFET with gate-drain underlap is investigated by numerical simulation. We validate that reducing drain doping concentration and increasing gate-drain underlap could be effective ways to reduce the off-state current and subthreshold swing (SS), while increasing source doping concentration and adjusting the composition of GaAs x Sb 1−x /In y Ga 1−y As can improve the on-state current. In addition, the resonant TFET based on GaAs x Sb 1−x /In y Ga 1−y As is also studied, and the result shows that the minimum and average of SS reach 11 mV/decade and 20 mV/decade for five decades of drain current, respectively, and is much superior to the conventional TFET.