Simultaneous Localization and Mapping (SLAM) technology, utilizing Light Detection and Ranging (LiDAR) sensors, is crucial for 3D environment perception and mapping. However, the absence of absolute observations and the inefficiency of single-robot perception present challenges for LiDAR SLAM in indoor environments. In this paper, we propose a multi-robot (MR) collaborative mapping method based on the Manhattan descriptor (MD) named MR-MD to overcome these limitations and improve the perception accuracy of LiDAR SLAM in indoor environments. The proposed method consists of two modules: MD generation and MD optimization. In the first module, each robot builds a local submap and constructs MD by parameterizing the planes in the submap. In the second module, the global main direction is updated using the historical MD of each robot, and constraints are built for each robot's horizontal and vertical directions according to their current MD and optimized. We conducted extensive comparisons with other multi-robot and single-robot LiDAR SLAM methods using real indoor data, and the results show that our method achieved higher mapping accuracy.