Aiming at the difficulty of wall-climbing robot in wall sensing and automated detection of large petrochemical equipment, an improved RTAB-Map (real-time appearance-based mapping) algorithm was proposed to realize the wall-climbing robot's localization, mapping and navigation by fusing multiple sensor data. Firstly, a robot motion chassis with wall adsorption ability was built to ensure the flexible and stable movement of the wall-climbing robot on the wall surface. Secondly, to address the cumulative error of the odometer resulting from the wall-climbing robot's slippage on the wall surface, the extended Kalman filter was utilized to fuse the data of encoder and inertial measurement unit to provide accurate odometer information for mapping and navigation. Thirdly, based on the RTAB-Map algorithm, the data of depth camera, LiDAR and odometer were fused to generate 2D grid and 3D point cloud map to realize a complete description of the equipment wall, and the navigation algorithm framework of the wall-climbing robot was constructed based on the fusion data. Finally, the experimental validation was carried out on the equipment wall. The results showed that the yaw angle error could be significantly reduced by using fusion mileage method, the average error of yaw angle was reduced by 88.94% compared with that under wheel odometer planning with an average error of 0.78°. The improved RTAB-Map algorithm improved the wall-climbing robot's mapping and sensing ability in the wall environment, and realized the autonomous navigation combined with the path planning algorithm. The research results have a certain reference significance for the research and application of automated detection technology of wall-climbing robots.