Tunneling field-effect transistors (TFETs) are very applicable to low standby-power application by their virtues of low off-current ($I_{off}$) and small subthreshold swing (S). However, low on-current ($I_{on}$) of silicon-based TFETs has been pointed out as a drawback. To improve $I_{on}$ of TFET, a gate-all-around (GAA) TFET based on III-V compound semiconductor with InAs/InGaAs/InP multiple-heterojunction structure is proposed and investigated. Its performances have been evaluated with the gallium (Ga) composition (x) for $In_{1-x}Ga_xAs$ in the channel region. According to the simulation results for $I_{on}$, $I_{off}$, S, and on/off current ratio ($I_{on}/I_{off}$), the device adopting $In_{0.53}Ga_{0.47}As$ channel showed the optimum direct-current (DC) performance, as a result of controlling the Ga fraction. By introducing an n-type InGaAs thin layer near the source end, improved DC characteristics and radio-frequency (RF) performances were obtained due to boosted band-to-band (BTB) tunneling efficiency.