Utilizing spin-orbit torque (SOT) to switch a magnetic moment provides a promising route for low-power-dissipation spintronic devices. Here, the SOT switching of a nearly compensated ferrimagnet Gdx(FeCo)1−x by the topological insulator [Bi2Se3 and (BiSb)2Te3] is investigated at room temperature. The switching current density of (BiSb)2Te3 (1.20 × 105 A cm−2) is more than one order of magnitude smaller than that in conventional heavy-metal-based structures, which indicates the ultrahigh efficiency of charge-spin conversion (>1) in topological surface states. By tuning the net magnetic moment of Gdx(FeCo)1−x via changing the composition, the SOT efficiency has a significant enhancement (6.5 times) near the magnetic compensation point, and at the same time the switching speed can be as fast as several picoseconds. Combining the topological surface states and the nearly compensated ferrimagnets provides a promising route for practical energy-efficient and high-speed spintronic devices.