News headline generation aims to produce a short sentence to attract readers to read the news. One news article often contains multiple keyphrases that are of interest to different users, which can naturally have multiple reasonable headlines. However, most existing methods focus on the single headline generation. In this paper, we propose generating multiple headlines with keyphrases of user interests, whose main idea is to generate multiple keyphrases of interest to users for the news first, and then generate multiple keyphrase-relevant headlines. We propose a multi-source Transformer decoder, which takes three sources as inputs: (a) keyphrase, (b) keyphrase-filtered article, and (c) original article to generate keyphrase-relevant, high-quality, and diverse headlines. Furthermore, we propose a simple and effective method to mine the keyphrases of interest in the news article and build a first large-scale keyphrase-aware news headline corpus, which contains over 180K aligned triples of <news article, headline, keyphrase>. Extensive experimental comparisons on the real-world dataset show that the proposed method achieves state-of-the-art results in terms of quality and diversity.