We investigate the motion of magnetic domain walls driven by magnetic fields and current-driven spin-orbit torques in an exchange-biased system with perpendicular magnetization. We consider Cr 2 O 3 /Co/Pt trilayers as a model system, in which the magnetization of the Co layer can be exchanged biased out-of-plane or inplane depending on the field-cooling direction. In field-driven experiments, the in-plane exchange bias favors the propagation of the domain walls with internal magnetization parallel to the exchange-bias field. In current-driven experiments, the domain walls propagate along the current direction, but the domain wall velocity increases and decreases symmetrically (antisymmetrically) for both current polarities when the exchange bias is parallel (perpendicular) to the current line. At zero external field, the exchange bias modifies the velocity of currentdriven domain wall motion by a factor of 10. We also find that the exchange bias remains stable under external fields up to 15 kOe and nanosecond-long current pulses with current density up to 3.5 × 10 12 A/m. Our results demonstrate versatile control of the domain wall motion by exchange bias, which is relevant to achieve fieldfree switching of the magnetization in perpendicular systems and current-driven manipulation of domain walls velocity in spintronic devices.