SLAM is the key technique for localization and surrounding perception in indoor environments. However, the dynamic posture adjustments of wheel-legged robots cast new challenges that affect the accuracy of localization. Therefore, this letter presents the Wheel-Legged SLAM, a novel indoor SLAM method for wheel-legged robots. The contributions of this research include the effective fusion of a dual LiDAR system for enhancing the robustness in degenerative indoor settings, the vertical correction factor for reducing the Z-axis drift and the gravity re-estimation factor for improving the pose accuracy. Extensive experiments in various indoor environments, including factories, corridors, and underground garages, demonstrate the robustness and accuracy of the proposed approach. The results indicate that the method proposed in this letter enhances the robustness of the LiDAR-inertial SLAM indoors, significantly improves the localization accuracy and reduces accumulative errors for the wheel-legged robot.