Recently, graph-based methods have been widely applied to model fitting. However, in these methods, association information is invariably lost when data points and model hypotheses are mapped to the graph domain. In this paper, we propose a novel model fitting method based on co-clustering on bipartite graphs (CBG) to estimate multiple model instances in data contaminated with outliers and noise. Model fitting is reformulated as a bipartite graph partition behavior. Specifically, we use a bipartite graph reduction technique to eliminate some insignificant vertices (outliers and invalid model hypotheses), thereby improving the reliability of the constructed bipartite graph and reducing the computational complexity. We then use a co-clustering algorithm to learn a structured optimal bipartite graph with exact connected components for partitioning that can directly estimate the model instances (i.e., post-processing steps are not required). The proposed method fully utilizes the duality of data points and model hypotheses on bipartite graphs, leading to superior fitting performance. Exhaustive experiments show that the proposed CBG method performs favorably when compared with several state-of-the-art fitting methods.