Manipulation of exchange bias (EB) via spin-current-induced spin–orbit torque (SOT) is of great importance in developing full electric control spintronic devices. Here, we report on SOT-dominant manipulation of the interfacial antiferromagnetic spins and the related perpendicular EB (PEB) in the IrMn/Co_{1- x}Tb _x (CoTb) bilayers with various Tb contents. No matter the magnetization of the ferrimagnetic CoTb layer is Co-dominant or Tb-dominant; all the samples were perpendicularly magnetized, and spontaneous PEB could be established during the isothermal crystallization of the IrMn layer. The SOT-induced EB switching could be accomplished with assistance of an in-plane or out-of-plane external magnetic field, associated with a monotonic reduction of the EB switching fraction by increasing x. This phenomenon is attributed to weakening of the interfacial exchange coupling between the CoTb and IrMn layers as x is increased. These findings provide a way to design high energy-efficient spintronic devices by employing the antiferromagnet/ferrimagnet bilayers, which may have weak stray field and strong robustness in contrast to commonly used heavy-metal/ferromagnet/antiferromagnet trilayers.