A typical approach to predicting unknown native structures of proteins is to assemble the amino acid residues (fragments) extracted from known structures. The quality of these extracted fragments, which are used to build protein-specific fragment libraries, can determine the success or failure of sampling near-native conformations. Here we show how a high-quality fragment library can be built using deep contextual learning techniques. Our algorithm, called DeepFragLib, employs bidirectional long short-term-memory recurrent neural networks with knowledge distillation for initial fragment classification, followed by an aggregated residual transformation network with cyclically dilated convolution for detecting near-native fragments. DeepFragLib improves the position-averaged proportion of near-native fragments by 12.2% over existing methods and, consequently, produces better near-native structures for 72.0% of the free-modelling domain targets tested when integrated with Rosetta. DeepFragLib is fully parallelized and available for use in conjunction with structure prediction programs.