This paper proposes a multi-UAV collaborative mapping system. The proposed method only uses LiDAR as sensor and can operate normally under extreme illumination conditions. In order to obtain precise relative pose between different UAVs which is required for map fusion, this paper develops a matching method based on UAVs’ historical trajectories. Once the UAV reaches the vicinity of the historical trajectory of other UAVs, coarse matching of local point cloud will be performed using brute force search. To obtain accurate positioning that satisfies map fusion, all overlapping point cloud of two UAVs will be extracted, and further optimization will be performed. Simulation has been performed under the gazebo environment. The result shows that the positioning accuracy of fused mapping is similar to that of independent mapping. The error of positioning is under 1.59%, which has verified the feasibility of the algorithm.