In this study, we present computational methods for predicting MHC-I epitope presentation with high accuracy and improved prediction of immunogenic neoepitopes. The BigMHC method comprises a large (51 million parameters), pan-allelic deep neural network trained on peptide-MHC presentation data from mass spectrometry assays and transfer learned on data from assays of antigen-specific immune response. Compared with NetMHCpan-4.1, PRIME, MHCflurry 2.0, MixMHCpred 2.1, MHCnuggets 2.3.2, and TransPHLA, BigMHC significantly improved the accuracy of predicting presented epitopes on a test set of 946,008 peptide-MHC complexes (AUROC=0.9838, AUPRC=0.9506). After transfer learning on immunogenicity data, BigMHC predicted immunogenic neoepitopes with the highest performance on independent test sets of neoepitopes validated for immunogenicity by IFN-γ release and MANAFEST assays. Moreover, BigMHC yielded significantly higher precision in identifying 215 immunogenic neoepitopes from a large (n=45,410,552) background of non-immunogenic epitopes, making BigMHC effective in clinical settings. All the data and codes are freely available at https://github.com/KarchinLab/bigmhc.