This paper develops a novel soft fault diagnosis approach for analog circuits. The proposed method employs the backward difference strategy to process the data, and a novel variant of convolutional neural network, i.e., convolutional neural network with global average pooling (CNN-GAP) is taken for feature extraction and fault classification. Specifically, the measured raw domain response signals are firstly processed by the backward difference strategy and the first-order and the second-order backward difference sequences are generated, which contain the signal variation and the rate of variation characteristics. Then, based on the one-dimensional convolutional neural network, the CNN-GAP is developed by introducing the global average pooling technical. Since global average pooling calculates each input vector’s mean value, the designed CNN-GAP could deal with different lengths of input signals and be applied to diagnose different circuits. Additionally, the first-order and the second-order backward difference sequences along with the raw domain response signals are directly fed into the CNN-GAP, in which the convolutional layers automatically extract and fuse multi-scale features. Finally, fault classification is performed by the fully connected layer of the CNN-GAP. The effectiveness of our proposal is verified by two benchmark circuits under symmetric and asymmetric fault conditions. Experimental results prove that the proposed method outperforms the existing methods in terms of diagnosis accuracy and reliability.