With the extensive application of analog circuits in many electronic devices, it is important to achieve accurate alerts in the incipient fault stage of analog circuits to reduce the threat on their reliability. However, the faint nature of incipient faults and the tolerance of components lead identifying incipient faults as a huge research challenge. Consequently, a complex convolutional self-attention autoencoder (CCSAE) is proposed in this paper to perform incipient fault diagnosis for analog circuits, which contains a feature extraction module, a feature enhancement module, and a classification module. In the first module, a backbone based on the complex convolutional autoencoder (CCAE) is designed to provide effective feature representations containing the amplitude information and phase information of analog circuit responses. In the feature enhancement module, a complex self-attention layer is constructed to enhance the useful structural information for feature representations by capturing internal correlations, thus addressing the faint nature of incipient faults. Finally, a two-step training mechanism including feature training and classification training is designed for CCSAE, where the key operation is the construction of supervised contrast loss (SCL) to pull closer similar feature representations and push away dissimilar ones. To demonstrate the effectiveness and merits of the proposed method, a typical Sallen-Key bandpass filter circuit and an actual amplifier board circuit of the water jet propulsion device are considered as experimental circuits. The experimental results indicate that this method achieves an average accuracy of 99.92% in the former and 98.25% in the latter, which is superior to other excellent methods.