Title: Towards Expressive Graph Representations for Graph Neural Networks. Abstract: Graph Neural Network (GNN) shows its powerful capability for graph representation learning in various application areas. However, most existing GNN variants learn the graph representations in a non-injective or non-continuous fashion, both reducing the model expressive power. In this paper, we present a theoretical framework to improve the expressive power of GNN by taking both injectivity and continuity into account. Accordingly, we develop \textit{Injective Continuous Graph Neural Network} (ICGNN) that learns the graph and node representations in an injective and continuous fashion, so that it can map similar nodes or graphs to similar embeddings, and non-equivalent nodes or non-isomorphic graphs to different embeddings. We validate the proposed ICGNN model for graph classification and node classification on multiple benchmark datasets including both simple graphs and attributed graphs. The experimental results demonstrate that our model achieves state-of-the-art performances on most of the benchmarks.