Recent studies have demonstrated that the excessive inflammatory response is an important factor of death in coronavirus disease 2019 (COVID-19) patients. In this study, we propose a deep representation on heterogeneous drug networks, termed DeepR2cov, to discover potential agents for treating the excessive inflammatory response in COVID-19 patients. This work explores the multi-hub characteristic of a heterogeneous drug network integrating eight unique networks. Inspired by the multi-hub characteristic, we design 3 billion special meta paths to train a deep representation model for learning low-dimensional vectors that integrate long-range structure dependency and complex semantic relation among network nodes. Based on the representation vectors and transcriptomics data, we predict 22 drugs that bind to tumor necrosis factor-α or interleukin-6, whose therapeutic associations with the inflammation storm in COVID-19 patients, and molecular binding model are further validated via data from PubMed publications, ongoing clinical trials and a docking program. In addition, the results on five biomedical applications suggest that DeepR2cov significantly outperforms five existing representation approaches. In summary, DeepR2cov is a powerful network representation approach and holds the potential to accelerate treatment of the inflammatory responses in COVID-19 patients. The source code and data can be downloaded from https://github.com/pengsl-lab/DeepR2cov.git.