Hadoop MapReduce is a framework for distributed computation on key-value pairs. The goal of this research is to verify actual running code of MapReduce applications. We first constructed an abstract model of MapReduce computation with the proof assistant Coq. In the model, mappers and reducers in MapReduce computation are modeled as functions in Coq, and a specification of a MapReduce application is expressed in terms of invariants among functions involving its mapper and reducer. The model also provides modular proofs of lemmas that do not depend on applications. To achieve the goal, we investigated the feasibility of two approaches. In one approach, we transformed verified mapper and reducer functions into Haskell programs and executed them under Hadoop Streaming. In the other approach, we verified JML annotations on Java programs of the mapper and reducer using Krakatoa, translated them into Coq axioms, and proved Coq specifications from them. In either approach, we were able to verify correctness of MapReduce applications that actually run on the Hadoop MapReduce framework.