Antibodies have the capacity to bind a diverse set of antigens, and they have become critical therapeutics and diagnostic molecules. The binding of antibodies is facilitated by a set of six hypervariable loops that are diversified through genetic recombination and mutation. Even with recent advances, accurate structural prediction of these loops remains a challenge. Here, we present IgFold, a fast deep learning method for antibody structure prediction. IgFold consists of a pre-trained language model trained on 558 million natural antibody sequences followed by graph networks that directly predict backbone atom coordinates. IgFold predicts structures of similar or better quality than alternative methods (including AlphaFold) in significantly less time (under 25 s). Accurate structure prediction on this timescale makes possible avenues of investigation that were previously infeasible. As a demonstration of IgFold's capabilities, we predicted structures for 1.4 million paired antibody sequences, providing structural insights to 500-fold more antibodies than have experimentally determined structures.