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Nowadays, deep learning methods, especially the Graph Convolutional Network (GCN), have shown impressive performance in hyperspectral image (HSI) classification. However, the current GCN-based methods treat graph construction and image classification as two separate tasks, which often results in suboptimal performance. Another defect of these methods is that they mainly focus on modeling the local pairwise importance between graph nodes while lack the capability to capture the global contextual information of HSI. In this paper, we propose a Multi-level GCN with Automatic Graph Learning method (MGCN-AGL) for HSI classification, which can automatically learn the graph information at both local and global levels. By employing attention mechanism to characterize the importance among spatially neighboring regions, the most relevant information can be adaptively incorporated to make decisions, which helps encode the spatial context to form the graph information at local level. Moreover, we utilize multiple pathways for local-level graph convolution, in order to leverage the merits from the diverse spatial context of HSI and to enhance the expressive power of the generated representations. To reconstruct the global contextual relations, our MGCN-AGL encodes the long range dependencies among image regions based on the expressive representations that have been produced at local level. Then inference can be performed along the reconstructed graph edges connecting faraway regions. Finally, the multi-level information is adaptively fused to generate the network output. In this means, the graph learning and image classification can be integrated into a unified framework and benefit each other. Extensive experiments have been conducted on three real-world hyperspectral datasets, which are shown to outperform the state-of-the-art methods.