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Multi-document summarization provides users with a short text that summarizes the information in a set of related documents. This paper introduces affinity-preserving random walk to the summarization task, which preserves the affinity relations of sentences by an absorbing random walk model. Meanwhile, we put forward adjustable affinity-preserving random walk to enforce the diversity constraint of summarization in the random walk process. The ROUGE evaluations on DUC 2003 topic-focused summarization task and DUC 2004 generic summarization task show the good performance of our method, which has the best ROUGE-2 recall among the graph-based ranking methods.