MOTIVATION: Prediction of peptide binding to the major histocompatibility complex (MHC) plays a vital role in the development of therapeutic vaccines for the treatment of cancer. Algorithms with improved correlations between predicted and actual binding affinities are needed to increase precision and reduce the number of false positive predictions. RESULTS: We present ACME (Attention-based Convolutional neural networks for MHC Epitope binding prediction), a new pan-specific algorithm to accurately predict the binding affinities between peptides and MHC class I molecules, even for those new alleles that are not seen in the training data. Extensive tests have demonstrated that ACME can significantly outperform other state-of-the-art prediction methods with an increase of the Pearson correlation coefficient between predicted and measured binding affinities by up to 23 percentage points. In addition, its ability to identify strong-binding peptides has been experimentally validated. Moreover, by integrating the convolutional neural network with attention mechanism, ACME is able to extract interpretable patterns that can provide useful and detailed insights into the binding preferences between peptides and their MHC partners. All these results have demonstrated that ACME can provide a powerful and practically useful tool for the studies of peptide-MHC class I interactions. AVAILABILITY AND IMPLEMENTATION: ACME is available as an open source software at https://github.com/HYsxe/ACME. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.