In this paper, we focus on the problem of keyword and document matching by considering different relevance levels. In our recommendation system, different people follow different hot keywords with interest. We need to attach documents to each keyword and then distribute the documents to people who follow these keywords. The ideal documents should have the same topic with the keyword, which we call topic-aware relevance. In other words, topic-aware relevance documents are better than partially-relevance ones in this application. However, previous tasks never define topic-aware relevance clearly. To tackle this problem, we define a three-level relevance in keyword-document matching task: topic-aware relevance, partially-relevance and irrelevance. To capture the relevance between the short keyword and the document at above-mentioned three levels, we should not only combine the latent topic of the document with its deep neural representation, but also model complex interactions between the keyword and the document. To this end, we propose a Two-stage Interaction and Topic-Aware text matching model (TITA). In terms of “topic-aware”, we introduce neural topic model to analyze the topic of the document and then use it to further encode the document. In terms of “two-stage interaction”, we propose two successive stages to model complex interactions between the keyword and the document. Extensive experiments reveal that TITA outperforms other well-designed baselines and shows excellent performance in our recommendation system.