The leakage of natural gas pipelines may cause significant safety accidents and cause severe economic losses to society. Therefore, timely detection and location of pipeline leak is an effective measure to reduce losses. Traditional methods need to extract the leak features from signals and then input them into convolutional neural networks to realize leakage diagnosis, which is a tedious process. This paper proposes a pipeline leak detection method based on residual connections and one-dimensional separable convolutional neural network (1D-RC-SCNN) and optimizes the structure and parameters of the model. The model uses one-dimensional separable convolution to replace the traditional convolutional neural network, which effectively reduces the number of model parameters. The improved residual connection can prevent the training data from overfitting and speed up the model convergence. The leakage signal after segmentation and preprocessing is directly sent to the 1D-RC-SCNN model, the leakage features are adaptively extracted, and then, the results are output through the Softmax classifier. The method directly performs end-to-end processing on the leaked signal, which improves the data processing speed. Finally, the cross-correlation method is used to locate the pipeline leak. The effectiveness of the proposed method is verified by building an experimental platform and compared with related models. The experimental results show that the method has high accuracy for the detection and localization of pipeline leak.