Most of the existing LiDAR-inertial odometry (LIO) methods are based on frame-to-map constraints, which may lead to inconsistency in state estimation. Approaches relying on frame-to-frame could address the inconsistency, but easily fail during association loss. In this article, HCF-LIO, a LIO algorithm based on a voxel-map-based hybrid constraint framework is proposed. The approach synergistically integrates single-frame absolute pose constraints (frame-to-map) with multiframe relative constraints (frame-to-frame) within a filtering architecture, effectively balancing short-term accuracy and long-term consistency. In addition, an implicit multiframe constraint approach based on probabilistic voxel map enables plane feature association without explicit tracking. Furthermore, a secondary motion compensation module is implemented after state update, enhancing the accuracy of the LiDAR point cloud map and the quality of multiframe association. To evaluate the proposed framework, extensive experiments and ablation studies are conducted on public datasets and private self-collected dataset. The experimental results demonstrate that HCF-LIO outperforms the state-of-the-art approaches in terms of accuracy and consistency while maintaining real-time operation.