Marine seismic interference noise occurs when energy from nearby marine seismic source vessels is recorded during a seismic survey. Such noise tends to be well preserved over large distances and causes coherent artefacts in the recorded data. Over the years, the industry has developed various denoising techniques for seismic interference removal, but although well performing, they are still time‐consuming in use. Machine‐learning‐based processing represents an alternative approach, which may significantly improve the computational efficiency. In the case of conventional images, autoencoders are frequently employed for denoising purposes. However, due to the special characteristics of seismic data as well as the noise, autoencoders failed in the case of marine seismic interference noise. We, therefore, propose the use of a customized U‐Net design with element‐wise summation as part of the skip‐connection blocks to handle the vanishing gradient problem and to ensure information fusion between high‐ and low‐level features. To secure a realistic study, only seismic field data were employed, including 25,000 training examples. The customized U‐Net was found to perform well, leaving only minor residuals, except for the case when seismic interference noise comes from the side. We further demonstrate that such noise can be treated by slightly increasing the depth of our network. Although our customized U‐Net does not outperform a standard commercial algorithm in quality, it can (after proper training) read and process one single shot gather in approximately 0.02 s. This is significantly faster than any existing industry denoising algorithm. In addition, the proposed network processes shot gathers in a sequential order, which is an advantage compared with industry algorithms that typically require a multi‐shot input to break the coherency of the noise.