Fault diagnosis techniques for analog circuits are widely applied in the diagnosis of electronic devices. It is of great significance to accurately and quickly find the fault location and the deviation of fault parameters in analog circuits. In this paper, we propose an innovative fault diagnosis approach for analog circuits. In this method, the wavelet packet transform (WPT) is employed to preprocess the time-domain response signals of analog circuit, and the proposed multi-channel one-dimensional residual networks (MC-1D-ResNet) is utilized for feature mining and fault diagnosis. Specifically, the two-level WPT is first carried out on the measured time-domain response signal to generate one approximate signal and three detailed signals. Additionally, the MC-1D-ResNet is developed by introducing a multi-channel structure based on 1D-ResNet, which can excavate and fuse various features from response signals and realize fault diagnosis. Through the simulation of the Sallen-key bandpass filter circuit and Four-opamp biquad high-pass filter circuit, the diagnostic reliability of this method has been fully verified. The results show that this method is very valuable for diagnosing faults of analog circuits and performs well on both test circuits. Even in the complex Four-opamp biquad high-pass filter circuit, the diagnostic accuracy can be up to 99.74%.