Traditional 3D light detection and ranging (LiDAR)-based simultaneous localization and mapping (SLAM) algorithms often encounter point cloud distortion and mismatching issues in degraded environments in which geometric features are sparse or absent, leading to decreased mapping and localization accuracy. To address these problems, this study proposes a LiDAR-inertial SLAM system based on continuous motion correction and intensity assistance. First, the system utilizes inertial measurement unit measurement data and spherical linear interpolation to correct point cloud distortion. Then, it leverages point cloud intensity information to extract geometric features in degraded environments, ultimately achieving high-precision self-localization and generating a globally consistent 3D map. Results of experiments using KITTI and SubT-MRS datasets show that the proposed method can realize LiDAR-based localization and mapping in degraded environments, with improvements in localization accuracy of 6.8% and 12.3%, respectively, compared to existing techniques. It also enables mapping with richer details in degraded environments.