The fault diagnosis of analog circuits faces problems, such as inefficient feature extraction and fault identification. To solve the problems, this paper combines the circle model and the extreme learning machine (ELM) into a fault diagnosis method for the linear analog circuit. Firstly, a circle model for the voltage features of fault elements was established in the complex domain, according to the relationship between the circuit response, element position and circuit topology. To eliminate the impacts of tolerances and signal aliasing, the 3D feature was introduced to make the indistinguishable features in fuzzy groups distinguishable. Fault feature separability is very important to improve the fault diagnosis accuracy. In addition, an effective classier can improve the precision and the time taken. With less computational complexity and a simpler process, the ELM algorithm has a fast speed and a good classification performance. The effectiveness of the proposed method is verified by simulation. The simulation results show the ELM-based algorithm classifier with the circle model can enhance precision and reduce time taken by about 80% in comparison with other methods for analog circuit fault diagnosis. To sum up, this proposed method offers a fault diagnosis method that reduces the complexity in generating fault features, improves the isolation probability of faults, speeds up fault classification, and simplifies fault testing.