Keyphrase extraction from documents is useful to a variety of applications such as information retrieval and document summarization. This paper presents an end-to-end method called DivGraphPointer for extracting a set of diversified keyphrases from a document. DivGraphPointer combines the advantages of traditional graph-based ranking methods and recent neural network-based approaches. Specifically, given a document, a word graph is constructed from the document based on word proximity and is encoded with graph convolutional networks, which effectively capture document-level word salience by modeling long-range dependency between words in the document and aggregating multiple appearances of identical words into one node. Furthermore, we propose a diversified point network to generate a set of diverse keyphrases out of the word graph in the decoding process. Experimental results on five benchmark data sets show that our proposed method significantly outperforms the existing state-of-the-art approaches.