This paper proposes a robust output feedback-fault tolerant control approach associated with the vibration suppression problem for active suspension subject to actuator fault and saturation, unavailable velocity signals, model uncertainty and external disturbance simultaneously. In this paper, an auxiliary system is introduced to solve the actuator saturation problem. The actuator fault, model uncertainty and external disturbance are treated as lumped disturbance. A novel estimator with finite-time convergence characteristics is proposed to estimate the unavailable velocity signals and lumped disturbance, and the disturbance compensation-based controller is designed with the reconstructed signals. In the process of controller design, a nominal controller is designed without lumped disturbance, and the nominal controller and finite-time estimator can be designed independently, so the controller gains can be selected flexibly. Rigorous theoretical analysis is carried out to confirm that all states of the closed-loop system are bounded. In the end, some experimental studies are conducted to show that the active suspension can be controlled effectively, and the efficacy and superiority of the designed method are verified.