An observer is presented for the simultaneous estimation of the system state and actuator and sensor faults of a discrete recurrent neural network (RNN) system. The presented approach enables disturbance attenuation and guarantees observer convergence. First, the discrete RNN is converted to a discrete linear parameter varying (LPV) model. Then, the LPV model is further transformed into a descriptor system by extending the system state and sensor fault. Next, an H-infinity observer is presented for the simultaneous estimation of the extended state and actuator fault of the descriptor system. Finally, the problem of observer design is translated into solving a linear matrix inequality. Experimental tests on a three-tank system have validated the effectiveness and correctness of the presented method.