Existing methods for single document summarization usually make use of only the information contained in the specified document. This paper proposes the technique of document expansion to provide more knowledge to help single document summarization. A specified document is expanded to a small document set by adding a few neighbor documents close to the document, and then the graphranking based algorithm is applied on the expanded document set for extracting sentences from the single document, by making use of both the within-document relationships between sentences of the specified document and the cross-document relationships between sentences of all documents in the document set. The experimental results on the DUC2002 dataset demonstrate the effectiveness of the proposed approach based on document expansion. The cross-document relationships between sentences in the expanded document set are validated to be very important for single document summarization.