Accurate positioning is important for improving the efficiency of repairing submarine cables and reducing the related repair costs. The magnetic anomaly produced by a submarine cable can be used to estimate its vertical and horizontal positions. A novel approach using magnetic data for estimating the position of submarine cables based on the 1D residual convolutional neural network (RCNN) is investigated. Infinitely long ferromagnetic cylinder models with different parameters are used to generate data sets for model training and testing. Tests on noisy synthetic data sets show that the developed 1D RCNN method can capture detailed features related to the magnetic source position information, which is more accurate than the conventional Euler method in estimating the position of submarine cables. The developed 1D RCNN method has also been successfully applied to processing field data. Furthermore, the processing workflow of our 1D RCNN method is less noise-sensitive compared with the conventional Euler method. The proposed 1D RCNN method and its workflow open a new window for estimating the position of submarine cables using magnetic data.