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Graph Neural Networks (GNNs) have received increasing attention in many fields. However, due to the lack of prior graphs, their use for semantic labeling has been limited. Here, we propose a novel architecture called the Self-Constructing Graph (SCG), which makes use of learnable latent variables to generate embeddings and to self-construct the underlying graphs directly from the input features without relying on manually built prior knowledge graphs. SCG can automatically obtain optimized non-local context graphs from complex-shaped objects in aerial imagery. We optimize SCG via an adaptive diagonal enhancement method and a variational lower bound that consists of a customized graph reconstruction term and a Kullback-Leibler divergence regularization term. We demonstrate the effectiveness and flexibility of the proposed SCG on the publicly available ISPRS Vaihingen dataset and our model SCG-Net achieves competitive results in terms of F1-score with much fewer parameters and at a lower computational cost compared to related pure-CNN based work. Our code will be made public soon.