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 stateactuator fault and sensor faultand completely decouple external disturbances.In the form of Linear Matrix Inequalities (LMI)the sufficient conditions for the existence of the observer are givenand it is proved that the error system is stable in finite time.Finallyanumerical simulation verifies the effectiveness of the proposed method.