Due to the sparsity and limited vertical resolution of 3D light detection and ranging (LiDAR) point clouds, LiDAR-inertial measurement unit (IMU) simultaneous localization and mapping (SLAM) systems often lack the effective elevation constraints and suffer from the accumulated vertical drift. To address this issue, this paper proposes a 3D LiDAR elevation-constrained SLAM method for autonomous vehicles by integrating ground curvature fitting with motion prediction. Ground points are first segmented with the spatial pre-filtering and reflectivity-based secondary filtering. Then the local ground points are fitted by a quadratic surface to estimate the ground normal vectors and average curvature, which are combined with predicted vehicle motion to construct a novel elevation constraint. The proposed elevation constraint factor together with LiDAR odometry and IMU pre-integration factors is incorporated into a factor graph optimization framework to achieve multi-source collaborative optimization while maintaining the real-time performance. Experiments on the KITTI dataset and a self-collected campus dataset demonstrate that the proposed method provides strong elevation constraints, reducing the average localization error by up to 46.54% compared to the tightly coupled LiDAR-inertial odometry algorithm via smoothing and mapping (LIO-SAM), which significantly improves the map consistency and trajectory stability.