Traditional anomaly detection on microblogging mostly focuses on individual anomalous users or messages. Since anomalous users employ advanced intelligent means, the anomaly detection is greatly poor in performance. In this paper, we propose an innovative framework of anomaly detection based on bipartite graph and co-clustering. A bipartite graph between users and messages is built to model the homogeneous and heterogeneous interactions. The proposed co-clustering algorithm based on nonnegative matrix tri-factorization can detect anomalous users and messages simultaneously. The homogeneous relations modeled by the bipartite graph are used as constraints to improve the accuracy of the co-clustering algorithm. Experimental results show that the proposed scheme can detect individual and group anomalies with high accuracy on a Sina Weibo dataset.