We present a phase-field based quantum transport study on the effect of the polarization multi-domain in the ferroelectric field-effect transistors (FE-FETs). The behavior of FEFETs is simulated by self-consistently solving the nonequilibrium Green's functions for carrier transport, Landau-Khalatnikov equations for polarization behavior with domain interactions, and Poisson's equations for the electrostatics of the whole device. We found that the drain-induced barrier lowering (DIBL) can be reduced in the case of FE-FETs, compared to the conventional MOSFETs with the high-kappa dielectric (HK FETs). As the gate length decreases, DIBL is more reduced, and so FE-FETs show significant performance improvement for short scaled devices, compared to HK FETs. We also found that the double-barrier-like channel potential profile can be induced by the multi-domain configuration. This gives rise to the direct source-to-drain tunneling leakage, causing the abrupt performance degradation. However, for extremely scaled FE-FETs, the polarization bound charge effect is weakened due to the reduction of the domain width, making the abrupt performance degradation disappear.