A secure control system is of great importance for unmanned aerial vehicles, especially in the condition of fault data injection. As the source of the feedback control system, the Inertial navigation system/Global position system (INS/GPS) is the premise of flight control system security. However, unmanned aerial vehicles have the requirement of lightweight and low cost for airborne equipment, which makes redundant device object unrealistic. Therefore, the method of fault detection and diagnosis is desperately needed. In this paper, a fault detection and diagnosis method based on fuzzy system and neural network is proposed. Fuzzy system does not depend on the mathematical model of the process, which overcomes the difficulties in obtaining the accurate model of unmanned aerial vehicles. Neural network has a strong self-learning ability, which could be used to optimize the membership function of fuzzy system. This paper is structured as follows: first, a Kalman filter observer is introduced to calculate the residual sequences caused by different sensor faults. Then, the sequences are transmitted to the fault detection and diagnosis system and fault type can be obtained. The proposed fault detection and diagnosis algorithm was implemented and evaluated with real datasets, and the results demonstrate that the proposed method can detect the sensor faults successfully with high levels of accuracy and efficiency.