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With the development of positioning technologies and the boosting deployment of inexpensive location-aware sensors, large volumes of trajectory data have emerged. However, efficient and scalable query processing over trajectory data remains a big challenge. We explore a new approach to this target in this paper, presenting a new framework for query processing over trajectory data based on MapReduce. Traditional trajectory data partitioning, indexing, and query processing technologies are extended so that they may fully utilize the highly parallel processing power of large-scale clusters. We also show that the append-only scheme of MapReduce storage model can be a nice base for handling updates of moving objects. Preliminary experiments show that this framework scales well in terms of the size of trajectory data set. It is also discussed the limitation of traditional trajectory data processing techniques and our future research directions.