To address the issues of height inaccuracy and ghost map caused by the vertical drift overlooked in existing LiDAR SLAM methods, a tightly coupled LiDAR-inertial SLAM method based on vertical constraints is proposed. This method extracts precise ground points by combining the installation height of the LiDAR sensor and the distance from points to the LiDAR. Based on the extracted ground points, a LiDAR odometry considering vertical residuals is designed. The method uses a two-step Levenberg-Marquardt (L-M) method to solve for pose transformation. These residuals contribute to converging to the optimal solution in the vertical direction. An Euclidean distance-based heuristic loop detection method is used to avoid ghost map. To verify the superiority of the proposed algorithm, relevant experiments were conducted in KITTI and in real-world scenarios. Experimental results demonstrate that compared to LeGO-LOAM, LIO-SAM and Point-LIO, the proposed method exhibits higher accuracy.