We propose a tunneling field-effect transistor (TFET) with a heteromaterial (HM)-gate not only for low standby power (LSTP) applications, which TFETs are genuinely suitable for, but also for high-speed performance by properly adjusting intrinsic gate capacitance (C(gg)). As a result of simulations in this work, the HM-gate TFET showed better subthreshold characteristics (smaller S) at an appropriate threshold voltage (V(th)) for LSTP applications, enhancing tunneling probability by modulating the difference in the metal workfunction (φ(m)) between the source-side gate (S-gate) and the drain-side gate (D-gate). Further, the C(gg) of HM-gate TFET were extracted and compared against that of conventional TFETs having gates with various φ(m)'s. Since lower C(gg) can be formed by high φ(m) in the D-gate, the HM-gate TFET has an excellent cut-off frequency (f(T)) and intrinsic delay time (τ) associated with the C(gg). We confirmed that the HM-gate TFET proposed in this work achieves superb performance for LSTP applications as well as high-frequency operations.