High-precision LiDAR odometry (LO) plays an essential role in autonomous driving. Generally, due to inaccurate data associations and the existence of outliers, it is a challenging task to estimate ego-motions reliably and efficiently given sparse and complexly distributed point clouds in outdoor environments. In this paper, we propose an unsupervised method for LiDAR odometry, named HPPLO-Net, to predict the relative pose of a LiDAR sensor in a hierarchical way. Specifically, we achieve accurate 6-DoF (Degree of Freedom) pose estimation between the source and target point clouds using a differentiable Point-to-Plane solver with the assistance of scene flow. The novel Point-to-Plane solver consists of a multi-scale aggregation (MSA) normal estimation layer and a differentiable weighted Point-to-Plane SVD module. The MSA layer is introduced to find reliable normal vectors of the pseudo target point cloud by aggregating multi-scale contextual information. The differentiable weighted Point-to-Plane SVD is embedded in the network to solve the pose matrix and alleviate the problem of lacking accurate data association in two LiDAR scans, which exists in the point-to-point alternatives. To reduce the impact of noises and outliers, our method can learn and update the inlier mask and the (residual) flow uncertainty at each layer of the hierarchy. We demonstrate the effectiveness of our method on the KITTI Odometry Dataset, Ford Campus Vision and Lidar DataSet, and the Apollo-SouthBay Dataset. Our method has achieved superior performance than recent unsupervised learning-based methods and some traditional geometry-based methods and has also achieved promising performance close to A-LOAM with mapping optimization. The source code of our method is available at https://github.com/IMRL/HPPLO-Net.