Based on their balance of movement flexibility, obstacle-surmounting ability, and load capacity, quadruped robots are increasingly employed in industrial inspections. Quadruped robots usually utilize laser simultaneous localization and mapping (SLAM) for autonomous navigation. However, SLAM coupled with legged odometry is susceptible to inaccuracies under the rapid movement and rotation of quadruped robots. To address this challenge, this article proposes a hybrid-dimensional laser SLAM framework for indoor quadruped robots that operates using only 3-D hybrid solid-state LiDAR and inertial measurement unit (IMU), eliminating the need to improve legged odometry accuracy, and adapts to any model of quadruped robot. The framework facilitates high-bandwidth and high-frequency dead-reckoning using laser inertial odometry (LIO) based on point-to-map matching. This prior for scan matching, along with motion blur removed, multiframe fused, and 2-D compressed LiDAR scans, are input into graph-based SLAM to obtain optimized pose estimations and 2-D grid maps. Optimized poses further enhance the accuracy of 3-D point cloud maps generated by LIO. The effectiveness of the framework is demonstrated through experiments conducted with the quadruped robot in simulated train depot inspection scenarios. Compared to graph-based SLAM without and with legged odometry as scan matching prior, the proposed framework exhibits enhanced mapping accuracy and repeated localization precision.