Li, Z.X., Xie, F., Ma, J.H., Qi, Z. and Wang, Y., 2023. CNN-based adaptive subtraction for the removal of seismic multiples. Journal of Seismic Exploration, 32: 169-184. In seismic data processing primaries are usually distorted by multiples which need to be removed in advance before seismic imaging. After multiple modelling, adaptive subtraction is essential for removing multiples successfully and can be expressed as a problem of linear regression (LR) with L1 norm minimization constraint on primaries or support vector regression (SVR). Compared to the LR-based method, the SVR-based method achieves better separation of primaries and multiples since it transforms the modelled multiples nonlinearly for a better match with the true multiples in every 2D data window. However, the LR- or SVR-based method may harm primaries or cause residual multiples in complex subsurface media. In this paper a deep convolutional neural network (CNN) is constructed to better express the complicated mismatches between the modelled multiples (input data) and true multiples of the original data (label) than the LR or SVR model. To avoid overfitting to the original data and preserve primaries the L1 norm minimization constraint on primaries and L2 norm minimization constraint on CNN coefficients are used in the optimization problem. During CNN training multiple 2D data windows constructed with one or several gathers are used simultaneously to avoid overfitting. The trained CNN is used in the corresponding training data to remove multiples and then the same flowchart with CNN is used in other gathers. The proposed CNN-based method extracts high-level features of the modelled multiples to remove multiples. It is demonstrated in the synthetic and field data examples that the proposed CNN-based method can better remove multiples and preserve primaries than the LR- or SVR-based method.