In this paper, we design and evaluate a new substructure-aware Graph Representation Learning (GRL) approach. GRL aims to map graph structure information into low-dimensional representations. While extensive efforts have been made for modeling global and/or local structure information, GRL can be improved by substructure information. Some recent studies exploit adversarial learning to incorporate substructure awareness, but hindered by unstable convergence. This study will address the major research question: is there a better way to integrate substructure awareness into GRL? As subsets of the graph structure, interested substructures (i.e., subgraph) are unique and representative for differentiating graphs, leading to the high correlation between the representation of the graph-level structure and substructures. Since mutual information (MI) is to evaluate the mutual dependence between two variables, we develop a MI inducted substructure-aware GRL method. We decompose the GRL pipeline into two stages: (1) node-level, where we introduce to maximize MI between the original and learned representation by the intuition that the original and learned representation should be highly correlated; (2) graph-level, where we preserve substructures by maximizing MI between the graph-level structure and substructure representation. Finally, we present extensive experimental results to demonstrate the improved performances of our method with real-world data.