Trailing-edge (TE) high-lift devices are commonly used to provide additional lift during takeoff and landing. Conventional high-subsonic civil transports primarily achieve lift increment by deflecting TE flaps to increase airfoil camber. However, for a supersonic civil transport (SCT) featuring a typical slender fuselage and high-swept, low-aspect-ratio wing configuration, a strong leading-edge (LE) vortex is induced from the smooth leading edge under low-speed, high-angle-of-attack conditions. In such cases, the deflection of TE flaps not only provides conventional lift but also enhances the intensity of the LE vortex, thereby contributing a vortex lift increment. Numerical simulations were conducted to systematically investigate the effects of different TE high-lift devices (including plain flaps, single-slotted flaps, and Fowler flaps) and their key design parameters (deflection angle, chord length, gap, and overlap) on the low-speed aerodynamic characteristics of an SCT in this work. The results indicate that, due to significant interference from the LE vortex, the TE flaps exhibit different aerodynamic characteristics in SCT under low-speed conditions compared to high-subsonic aircraft. The increase in the deflection angle of the TE flaps not only enhances their own lift contribution but also strengthens the LE vortex, significantly increasing the vortex lift over the main wing. However, the enhanced LE vortex may promote earlier vortex breakdown, thus advancing stall onset. Specifically, the LE vortex exacerbates flow separation in the rear region of slotted high-lift configurations (single-slotted and Fowler flaps), thereby reducing their lift-enhancement efficiency, so the low-speed aerodynamic characteristics of the SCT are insensitive to both the slot parameters (gap and overlap) and the chord length of the TE flap in the present work.