Given a graph G and a query node q, community search (CS) seeks a cohesive subgraph from G that contains q. CS has gained much research interests recently. In the database research community, researchers aim to find the most cohesive subgraph satisfying a specific community model (e.g., k-core or k-truss) via graph traversal. These works obtain good precision, however suffering from the low efficiency issue. In the AI research community, a new thought of using the deep learning model to support CS without relying on graph traversal emerges. Supervised end-to-end models using GCN are presented, which perform efficiently, but leave a large room for precision improvement. None of them can achieve a good balance between the efficiency and effectiveness. This motivates our solution: First, we present an offline community-injected graph embedding method to preserve the community’s cohesiveness features into the learned node representations. Second, we resort to a proximity graph (PG) built from node representations, to quickly return the community online. Moreover, we develop a self-augmented method based on KL divergence to further optimize node representations. Extensive experiments on seven real-world graphs show our solution’s superiority on effectiveness (at least 39.3% improvement) and efficiency (one to two orders of magnitude faster).