Robotic building inspection is gaining popularity as a way to increase the security, productivity, and cost-effectiveness of traditional inspection tasks. Despite the development of numerous building inspection robotic platforms, their motions still require manual control. To facilitate full automation, there is a need to explore autonomous navigation strategies for building inspection robots. Although various autonomous navigation strategies have been developed in the robotics field, few of them are suitable for building structural inspection behavior. In accordance with the responsibilities of professional inspectors, the robot is required to follow the structural components within a desired distance and dynamically avoid obstacles to conduct in-depth scanning. This navigation task becomes more difficult when providing smooth following path in special building scenarios, such as narrow corners. Motivated by this need, the present study aimed to explore autonomous navigation for building inspection robots. To save the cost of map construction, the local navigation strategies, which control the robots' travel in unknown environments, were targeted.Specifically, the objective is to develop a robust fuzzy logic controller (FLC) for wall-following behavior. The inputs are the distances within the designed interval ranges, which were measured with a 360-degree laser. The membership functions and the decision-making rules were designed based on robot and camera configurations, building designs, and structural inspection criteria. The outputs are the real-time angular and linear velocities. Tested in both simulation and real-world environments, the novelty of the designed FLC is: 1) enabling "finding wall," "wall-following," "turning," and "obstacle avoidance" behaviors in various unknown building scenarios; 2) preventing wavy motions; and 3) preventing path deviations for arbitrary surfaces. The results can be employed to perform daily structural inspections, and they are dedicated to automating the building inspection tasks. However, the FLC is sensitive to the reflective components because of the limitations of the position sensors.