Abstract: The field of nuclear applications has always prioritized nuclear safety. A contemporary development in this area is the use of mobile robots possessing nuclear radiation detection sensors, replacing traditional manual detection methods. We propose an autonomous radiation map construction framework based on Lidar-Visual-Inertial odometry via Smoothing and Mapping(LVI-SAM) to solve the problem of localizing and monitoring surface radiation sources in an unknown three-dimensional (3D) environment using mobile robots equipped with LiDAR, cameras, inertial measurement units, and radiation detection sensors instead of manual radiation monitoring. The map construction framework merges simultaneous localization and mapping technology with radiation detection technology. Moreover, the map construction framework uses LiDAR and visual information to recreate the environment in three dimensions under the LVI-SAM framework. Then, the framework builds a raster map of the environment by downscaling and projecting the 3D point cloud. The position of the radiation source in the scene is acquired by using radiation sensors and the changed relationship of the LVI-SAM coordinate system. This approach fuses the radiation map and the 3D environment map; consequently, it facilitates the localization of the radiation area in the 3D environment. The experimental results of establishing a simulation environment in a robot operating system validate the effectiveness of building surface radiation maps in a 3D environment.