This paper proposes a fault diagnosis method based on system identification and self-adaptive neural network for a class of SISO systems with system identification. In the case of system with noise and other external disturbances, the least squares method is first used for the SISO system, and conduct online modeling. On this basis, the observer is used to observe the nonlinear function. In order to ensure the stability of the observer and the diagnosis system, the stability of the closed-loop system under bounded noise interference and system uncertainty is given.