In many real applications such as the data integration, social network analysis, and the Semantic Web, the entity resolution (ER) is an important and fundamental problem, which identifies and links the same real-world entities from various data sources. While prior works usually consider ER over static and complete data, in practice, application data are usually collected in a streaming fashion, and often incur missing attributes (due to the inaccuracy of data extraction techniques). Therefore, in this paper, we will formulate and tackle a novel problem, topic-aware entity resolution over incomplete data streams (TER-iDS), which online imputes incomplete tuples and detects pairs of topic-related matching entities from incomplete data streams. In order to effectively and efficiently tackle the TER-iDS problem, we propose an effective imputation strategy, carefully design effective pruning strategies, as well as indexes/synopsis, and develop an efficient TER-iDS algorithm via index joins. Extensive experiments have been conducted to evaluate the effectiveness and efficiency of our proposed TER-iDS approach over real data sets.