The intelligent inspection robots can complete the inspection task efficiently and reliably, and reduce the labor intensity of staff. Accurate and stable navigation positioning is the basis for inspection tasks of inspection robots. A navigation system based on light detection and ranging (LiDAR) was developed to achieve mapping, path planning and navigation positioning of the robot in both indoor and outdoor environments. The navigation system was composed of remote monitoring platform and inspection robot. The remote monitoring platform can issue inspection tasks, monitor robot status, query and store detection data, while the inspection robot can conduct navigation and positioning autonomously, traverse detection point, complete data acquisition and other inspection tasks. The platform and inspection robot exchanged remote data through wireless network. To build the 2D environment map, the information from LiDAR and encoder was combined by using a robust Gmapping algorithm. Based on the information of the map and detection points, the branch-and-bound algorithm was applied to search the optimal inspection route in order to reduce inspection time and energy consumption. Adaptive Monte Carlo localization (AMCL) algorithm was used to estimate the position and posture of the robot. The navigation and positioning was achieved by combining the position, posture and the inspection route calculated previously. Robot driver control was completed based on classic PID algorithm with the input of lateral deviation and heading deviation. The robot was equipped with RGB camera and IR camera, and targets can be detected more efficiently using the fusion information of visible and infrared images. In order to verify the accuracy of the navigation system, the indoor navigation positioning experiment was carried out in this research. With the speed of 1m/s, the mean absolute error (MAE) of the position and heading deviation was less than 5cm and 1.1° and the standard deviation (SD) was less than 5cm and 1.5°, which can meet the requirements of inspection navigation and positioning.