Abstract: This study focuses on the finite-time fault estimation observer and fault-tolerant controller design for one-sided Lipschitz Markovian jump systems including generally uncertain transition rates. First, we propose an adaptive finite-time fault estimation observer, which is robust to unknown input, that can simultaneously estimate the states and actuator and sensor faults and ensure that the error dynamics is H_∞ finite-time-bounded. Then, on the basis of the estimated states and actuator fault, a finite-time fault-tolerant control strategy is designed to guarantee the H_∞ finite-time-boundedness of the closed-loop system. Sufficient conditions for the existence of the designed finite-time observer and controller are obtained in terms of linear matrix inequalities. Finally, a practical example is given to show the validation of the proposed method.