Graph embedding methods transform high-dimensional and complex graph contents into low-dimensional representations. They are useful for a wide range of graph analysis tasks including link prediction, node classification, recommendation and visualization. Most existing approaches represent graph nodes as point vectors in a low-dimensional embedding space, ignoring the uncertainty present in the real-world graphs. Furthermore, many real-world graphs are large-scale and rich in content (e.g. node attributes). In this work, we propose GLACE, a novel, scalable graph embedding method that preserves both graph structure and node attributes effectively and efficiently in an end-to-end manner. GLACE effectively models uncertainty through Gaussian embeddings, and supports inductive inference of new nodes based on their attributes. In our comprehensive experiments, we evaluate GLACE on real-world graphs, and the results demonstrate that GLACE significantly outperforms state-of-the-art embedding methods on multiple graph analysis tasks.