Simultaneous localization and mapping (SLAM) technology based on light detection and ranging (LiDAR) sensors has been widely used in various environmental sensing tasks indoors and outdoors. However, it still lacks effective constraints in structured environments such as corridors and parking lots, and its accuracy needs improvement. Based on this, a planar constraint-assisted LiDAR SLAM algorithm based on the Manhattan World (MW) assumption is proposed in this paper. The algorithm extracts planes from the environment point cloud submap, classifies the planes according to the ground and vertical planes, and calculates the main direction angles of the ground and vertical plane, respectively, to construct constraints. To enhance the stability and robustness of the system, a two-step main direction angle calculation and update strategy are designed, and a hysteresis update is used to avoid the introduction of errors by unoptimized planes. This paper uses a backpack laser scanning system to collect experimental data in various scenes. These data are used to compare our method with three open-source LiDAR SLAM algorithms, that are currently more widely used and perform better. Qualitative and quantitative experiments are conducted to verify the effectiveness of our method. The experimental results show that the absolute accuracy of the point clouds obtained by our method is improved by 77.46% on average compared with the other three algorithms in the environment, conforming to the MW assumption, which verifies the effectiveness of the algorithm.