Attribute graphs are ubiquitous in multimedia applications, and graph representation learning (GRL) has been successful in analyzing attribute graph data. However, incomplete graph data and missing node attributes can have a negative impact on media knowledge discovery. Existing methods for handling attribute missing graph have limited assumptions or fail to capture complex attribute-graph dependencies. To address these challenges, we propose Attribute missing Graph Contrastive Learning (AmGCL), a framework for handling missing node attributes in attribute graph data. AmGCL leverages Dirichlet energy minimization-based feature precoding to encode in missing attributes and a self-supervised Graph Augmentation Contrastive Learning Structure (GACLS) to learn latent variables from the encoded-in data. Specifically, AmGCL utilizies feature reconstruction based on structure-attribute energy minimization while maximizes the lower bound of evidence for latent representation mutual information. Our experimental results on multiple real-world datasets demonstrate that AmGCL outperforms state-of-the-art methods in both feature imputation and node classification tasks, indicating the effectiveness of our proposed method in real-world attribute graph analysis tasks.