The traditional back-propagation algorithm has some disadvantages, for instance, the speed of learning convergence is too slow and local extreme values are present in the process of search sometimes. In order to solve the problems described above, this paper applies adaptive learning rate and momentum term to improve the general back-propagation algorithm. Taking the circuit system's fault diagnosis for example, the basic fault features are transformed by means of using the fuzzy sets of fuzzy mathematics, and take as the inputs of the adaptive neural network. And then, the fault codes are used as the outputs of adaptive neural network. The experiment simulation results show that this method can be used to diagnose and identify the fault types of circuit system effectively.