Graph representation learning is a fundamental research issue in various domains of applications, of which the inductive learning problem is particularly challenging as it requires models to generalize to unseen graph structures during inference. In recent years, graph neural networks (GNNs) have emerged as powerful graph models for inductive learning tasks such as node classification, whereas they typically heavily rely on the annotated nodes under a fully supervised training setting. Compared with the GNN-based methods, variational graph auto-encoders (VGAEs) are known to be more generalizable to capture the internal structural information of graphs independent of node labels and have achieved prominent performance on multiple unsupervised learning tasks. However, so far there is still a lack of work focusing on leveraging the VGAE framework for inductive learning, due to the difficulties in training the model in a supervised manner and avoiding over-fitting the proximity information of graphs. To solve these problems and improve the model performance of VGAEs for inductive graph representation learning, in this work, we propose the Self-Label Augmented VGAE model. To leverage the label information for training, our model takes node labels as one-hot encoded inputs and then performs label reconstruction in model training. To overcome the scarcity problem of node labels for semi-supervised settings, we further propose the Self-Label Augmentation Method (SLAM), which uses pseudo labels generated by our model with a node-wise masking approach to enhance the label information. Experiments on benchmark inductive learning graph datasets verify that our proposed model archives promising results on node classification with particular superiority under semi-supervised learning settings.