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Topic drift is a common phenomenon in multi-turn dialogue. Therefore, an ideal dialogue generation models should be able to capture the topic information of each context, detect the relevant context, and produce appropriate responses accordingly. However, existing models usually use word or sentence level similarities to detect the relevant contexts, which fail to well capture the topical level relevance. In this paper, we propose a new model, named STAR-BTM, to tackle this problem. Firstly, the Biterm Topic Model is pre-trained on the whole training dataset. Then, the topic level attention weights are computed based on the topic representation of each context. Finally, the attention weights and the topic distribution are utilized in the decoding process to generate the corresponding responses. Experimental results on both Chinese customer services data and English Ubuntu dialogue data show that STAR-BTM significantly outperforms several state-of-the-art methods, in terms of both metric-based and human evaluations.