In this paper, we propose to query correlated graphs in a data stream scenario, where an algorithm is required to retrieve the top k graphs which are mostly correlated to a query graph q. Due to the dynamic changing nature of the stream data and the inherent complexity of the graph query process, treating graph streams as static datasets is computationally infeasible or ineffective. In the paper, we propose a novel algorithm, Hoe-PGPL, to identify top-k correlated graphs from data stream, by using a sliding window which covers a number of consecutive batches of stream data records. Our theme is to employ Hoeffding bound to discover some potential candidates and use two level candidate checking (one corresponding to the whole sliding window level and one corresponding to the local data batch level) to accurately estimate the correlation of the emerging candidate patterns, without rechecking the historical stream data. Experimental results demonstrate that the proposed algorithm not only achieves good performance in terms of query precision and recall, but also is several times, or even an order of magnitude, more efficient than the straightforward algorithm with respect to the time and the memory consumption. Our method represents the first research endeavor for data stream based top-k correlated graph query.