In recent years, deep models have achieved remarkable success in many vision tasks. Unfortunately, their performance largely depends on intensive training samples. In contrast, human beings typically perform hybrid learning, e.g., spontaneously integrating structured knowledge for cross-domain recognition or on a much smaller amount of data samples for few-shot learning. Thus it is very attractive to extend hybrid learning for the computer vision tasks by seamlessly integrating structured knowledge with data samples to achieve more effective representation learning. However, such a hybrid learning approach remains a great challenge due to the huge gap between the structured knowledge and the deep features (learned from data samples) on both dimensions and knowledge granularity. In this paper, a novel Epistemic Graph Layer (EGLayer) is developed to enable hybrid learning, such that the information can be exchanged more effectively between the deep features and a structured knowledge graph. Our EGLayer is composed of three major parts: (a) a local graph module to establish a local prototypical graph through the learned deep features, i.e., aligning the deep features with the structured knowledge graph at the same granularity; (b) a query aggregation model to aggregate useful information from the local graphs, and using such representations to compute their similarity with global node embeddings for final prediction; and (c) a novel correlation loss function to constrain the linear consistency between the local and global adjacency matrices.