The progress in Query-focused Multi-Document Summarization (QMDS) has been limited by the lack of sufficient largescale high-quality training datasets. We present two QMDS training datasets, which we construct using two data augmentation methods: (1) transferring the commonly used single-document CNN/Daily Mail summarization dataset to create the QMDSCNN dataset, and (2) mining search-query logs to create the QMDSIR dataset. These two datasets have complementary properties, i.e., QMDSCNN has real summaries but queries are simulated, while QMDSIR has real queries but simulated summaries. To cover both these real summary and query aspects, we build abstractive end-to-end neural network models on the combined datasets that yield new state-of-the-art transfer results on DUC datasets. We also introduce new hierarchical encoders that enable a more efficient encoding of the query together with multiple documents. Empirical results demonstrate that our data augmentation and encoding methods outperform baseline models on automatic metrics, as well as on human evaluations along multiple attributes.