As a key technology for autonomous navigation and positioning in mobile robots, light detection and ranging (LiDAR) odometry is widely used in autonomous driving applications. The Iterative Closest Point (ICP)-based methods have become the core technique in LiDAR odometry due to their efficient and accurate point cloud registration capability. However, some existing ICP-based methods do not consider the reliability of the initial pose, which may cause the method to converge to a local optimum. Furthermore, the absence of an adaptive mechanism hinders the effective handling of complex dynamic environments, resulting in a significant degradation of registration accuracy. To address these issues, this paper proposes an adaptive ICP-based LiDAR odometry method that relies on a reliable initial pose. First, distributed coarse registration based on density filtering is employed to obtain the initial pose estimation. The reliable initial pose is then selected by comparing it with the motion prediction pose, reducing the initial error between the source and target point clouds. Subsequently, by combining the current and historical errors, the adaptive threshold is dynamically adjusted to accommodate the real-time changes in the dynamic environment. Finally, based on the reliable initial pose and the adaptive threshold, point-to-plane adaptive ICP registration is performed from the current frame to the local map, achieving high-precision alignment of the source and target point clouds. Extensive experiments on the public KITTI dataset demonstrate that the proposed method outperforms existing approaches and significantly enhances the accuracy of LiDAR odometry.