Graph has been widely used in various applications, while how to optimize the graph is still an open question. In this paper, we propose a framework to optimize the graph structure via structure evolution on graph manifold. We first define the graph manifold and search the best graph structure on this manifold. Concretely, associated with the data features and the prediction results of a given task, we define a graph energy to measure how the graph fits the graph manifold from an initial graph structure. The graph structure then evolves by minimizing the graph energy. In this process, the graph structure can be evolved on the graph manifold corresponding to the update of the prediction results. Alternatively iterating these two processes, both the graph structure and the prediction results can be updated until converge. It achieves the suitable structure for graph learning without searching all hyperparameters. To evaluate the performance of the proposed method, we have conducted experiments on eight datasets and compared with the recent state-of-the-art methods. Experiment results demonstrate that our method outperforms the state-of-the-art methods in both transductive and inductive settings.