Motivation: With the rapidly growing biomedical literature, automatically indexing biomedical articles by Medical Subject Heading (MeSH), namely MeSH indexing, has become increasingly important for facilitating hypothesis generation and knowledge discovery. Over the past years, many large-scale MeSH indexing approaches have been proposed, such as Medical Text Indexer, MeSHLabeler, DeepMeSH and MeSHProbeNet. However, the performance of these methods is hampered by using limited information, i.e. only the title and abstract of biomedical articles. Results: We propose FullMeSH, a large-scale MeSH indexing method taking advantage of the recent increase in the availability of full text articles. Compared to DeepMeSH and other state-of-the-art methods, FullMeSH has three novelties: (i) Instead of using a full text as a whole, FullMeSH segments it into several sections with their normalized titles in order to distinguish their contributions to the overall performance. (ii) FullMeSH integrates the evidence from different sections in a 'learning to rank' framework by combining the sparse and deep semantic representations. (iii) FullMeSH trains an Attention-based Convolutional Neural Network for each section, which achieves better performance on infrequent MeSH headings. FullMeSH has been developed and empirically trained on the entire set of 1.4 million full-text articles in the PubMed Central Open Access subset. It achieved a Micro F-measure of 66.76% on a test set of 10 000 articles, which was 3.3% and 6.4% higher than DeepMeSH and MeSHLabeler, respectively. Furthermore, FullMeSH demonstrated an average improvement of 4.7% over DeepMeSH for indexing Check Tags, a set of most frequently indexed MeSH headings. Availability and implementation: The software is available upon request.