Document databases are increasingly popular in various applications, but their queries are challenging to write due to the flexible and complex data model underlying document databases. This paper presents a synthesis technique that aims to generate document database queries from input-output examples automatically. A new domain-specific language is designed to express a representative set of document database queries in an algebraic style. Furthermore, the synthesis technique leverages a novel abstraction of collections for deduction to efficiently prune the search space and quickly generate the target query. An evaluation of 110 benchmarks from various sources shows that the proposed technique can synthesize 108 benchmarks successfully. On average, the synthesizer can generate document database queries from a small number of input-output examples within tens of seconds.