We present a novel graph memory structure for navigation, called Frontier-enhanced Topological Memory (FTM). Most prior research primarily focuses on maintaining memory representations for explored areas. In contrast, our approach incorporates ghost nodes into the topological map to characterize unexplored but visible regions. The ghost nodes are generated using a geometric method and serve to indicate the geometrically explorable frontiers, thereby promoting agent's exploration and target search. We employ an online-trained implicit representation method to predict perceptual features for ghost nodes based on previous observations. In addition, we develop a Multi-Stage Memory Extraction module (MSME) that can effectively utilize the FTM. It focuses particularly on task-specific information and generates actions end-to-end. By using FTM, the agent can improve its capacity for environmental cognition and memory utilization. We evaluate the proposed approach on visual navigation in the photo-realistic Gibson environment. Experimental results conclusively demonstrate that the proposed navigation framework with FTM boosts the agent's exploration awareness and enhances the performance in image-goal navigation tasks.