The goal of query-focused summarization is to extract a summary for a given query from the document collection. Although much work has been done for this problem, there are still many challenging issues: (1) The length of the summary is predefined by, for example, the number of word tokens or the number of sentences. (2) A query usually asks for information of several perspectives (topics); however existing methods cannot capture topical aspects with respect to the query. In this paper, we propose a novel approach by combining statistical topic model and affinity propagation. Specifically, the topic model, called qLDA, can simultaneously model documents and the query. Moreover, the affinity propagation can automatically discover key sentences from the document collection without predefining the length of the summary. Experimental results on DUC05 and DUC06 data sets show that our approach is effective and the summarization performance is better than baseline methods.