A reduced-order observer is designed for a class of T-S Semi-Markovian Jump Systems (S-MJSs) with general uncertain transition rates.It can simultaneously estimate the system stateactuator fault and sensor faultand completely decouple external disturbances.In the form of Linear Matrix Inequalities (LMI)the sufficient conditions for the existence of the observer are givenand it is proved that the error system is stable in finite time.Finallyanumerical simulation verifies the effectiveness of the proposed method.