Query relevance ranking and sentence saliency ranking are the two main tasks in extractive query-focused summarization. Previous supervised summarization systems often perform the two tasks in isolation. However, since reference summaries are the trade-off between relevance and saliency, using them as supervision, neither of the two rankers could be trained well. This paper proposes a novel summarization system called AttSum, which tackles the two tasks jointly. It automatically learns distributed representations for sentences as well as the document cluster. Meanwhile, it applies the attention mechanism to simulate the attentive reading of human behavior when a query is given. Extensive experiments are conducted on DUC query-focused summarization benchmark datasets. Without using any hand-crafted features, AttSum achieves competitive performance. We also observe that the sentences recognized to focus on the query indeed meet the query need.