Due to the importance and efficiency of learning complex structures hidden in data, graph-based methods have been widely studied and get successful in unsupervised learning. Generally, most existing graph-based clustering methods require post-processing on the original data graph to extract the clustering indicators. However, there are two drawbacks with these methods: (1) the cluster structures are not explicit in the clustering results; (2) the final clustering performance is sensitive to the construction of the original data graph. To solve these problems, in this paper, a novel learning model is proposed to learn a graph based on the given data graph such that the new obtained optimal graph is more suitable for the clustering task. We also propose an efficient algorithm to solve the model. Extensive experimental results illustrate that the proposed model outperforms other state-of-the-art clustering algorithms.