Reliably navigating to a distant goal remains a major challenge in robotics. In contrast, animals such as rats and pigeons can perform goal-directed navigation with great reliability. Evidence from neural science and ethology suggests that various species represent the spatial space as a topological template, with which they can actively evaluate future navigation uncertainty and plan reliable/safe paths to distant goals. While topological navigation models have been deployed in mobile robots, relatively little inspiration has drawn upon biology in terms of topological mapping and active path planning. In this paper, we propose a novel bio-inspired topological navigation model, which consists of topological map construction, active path planning and path execution, for aerial mobile robots with visual landmark recognition and compass orientation capability. To mimic the topological spatial representation, the model firstly builds the topological nodes based on the reliability of visual landmarks, and constructs the edges based on the compass accuracy. Then a reward diffusion algorithm akin to animals’ path evaluation process is developed. The diffusion process takes the topological structure and landmark reliability into consideration, which helps the agent to construct the path with visually reliable nodes. In the path execution process, the agent combines orientation guidance and landmark recognition to estimate its position. To evaluate the performance of the proposed navigation model, a systematic series of experiments were conducted in a range of challenging and varied real-world visual environments. The results show that the proposed model generates animal-like navigation behaviours, which avoids travelling across large visually aliased areas, such as forest and water regions, and achieves higher localization accuracy than navigating on the shortest paths.