The brain navigates mazes using the entorhinal grid and hippocampal place codes. While specific grid codes can represent maze structures independent of behavioral policy, little is known about how these task structure-specific grid codes generalize to novel tasks requiring different structures and policies. Reinforcement learning algorithms typically employ policy-biased representations, yet this approach lacks biological plausibility since it requires multiple distinct representations for task completion. To address these limitations, we propose topology-aware grid coding (TAG), a novel computational theory that leverages environmental topology for generalization across new structures and reward configurations. First, we demonstrate that policy-unbiased grid codes are essential for encoding environment topology. The TAG model achieves this by unifying place, border, and corner codes. While place codes guide navigation, TAG exploits border codes to compute structural state prediction errors (SPE) for learning unbiased grid codes, and corner codes to identify topologically significant states. Our findings are summarized as follows: We demonstrate the topology awareness of TAG grid codes through their robustness to topologically homeomorphic environmental augmentations while maintaining sensitivity to distinguishing between non-isomorphic environments. TAG exhibited the fastest learning speed and the most robust performance in developing unbiased grid codes for novel environmental structures, regardless of exploration policy. TAG rapidly adapts to novel environmental structures by leveraging topological priors during exploration. By utilizing both high and low discount factors---which balance structure and policy encoding---the model enables efficient navigation with multiple subgoals without requiring extensive planning. Our work proposes an efficient computational principle of hippocampal topology encoding and advances our understanding of hippocampal information processing.