Replication is a method to keep the consistency of source data and target data. In our previous work of access-aware in-memory data cache middleware for relational databases, the data are easy to be lost in case that power cuts off. Therefore, we investigate a live data replication approach from in-memory data cache to versioning repository in this paper. This method attempts to recover the in-memory data cache from the versioning repository in failure of access-aware in-memory data cache middleware. Although the replication is not a new problem, the state of art of the replication in the context of document stores is not mature. In our paper, we propose a live data replication approach of in-memory document stores using stream processing framework.First, we introduce cell state model to describe the replication process. To infinitely look back to any revision, we enable our proposed cell state model to support copy-modify-merge model to manage the changed data revisions subsequently. Finally, experimental results show that this approach is more suitable for the replication of continuous in-stream changed data compared with MapReduce-based batch replication.