We present NegativeRank, a novel graph-based sentence ranking model to improve the diversity of focused summary by performing random walks over sentence graph with negative edge weights. Unlike the typical eigenvector centrality ranking, our method models the redundancy among sentence nodes as the negative edges. The negative edges can be thought of as the propagation of disapproval votes which can be used to penalize redundant sentences. As the iterative process continues, the initial ranking score of a given node will be adjusted according to a long-term negative endorsement from other sentence nodes. The evaluation results confirm that our proposed method is very effective in improving the diversity of the focused summary, compared to several well-known text summarization methods.