An efficient 3D point cloud learning architecture, named PWCLO-Net, for LiDAR odometry is first proposed in this paper. In this architecture, the projection-aware representation of the 3D point cloud is proposed to organize the raw 3D point cloud into an ordered data form to achieve efficiency. The Pyramid, Warping, and Cost volume (PWC) structure for the LiDAR odometry task is built to estimate and refine the pose in a coarse-to-fine approach hierarchically and efficiently. A projection-aware attentive cost volume is built to directly associate two discrete point clouds and obtain embedding motion patterns. Then, a trainable embedding mask is proposed to weigh the local motion patterns to regress the overall pose and filter outlier points. The trainable pose warp-refinement module is iteratively used with embedding mask optimized hierarchically to make the pose estimation more robust for outliers. The entire architecture is holistically optimized end-to-end to achieve adaptive learning of cost volume and mask, and all operations involving point cloud sampling and grouping are accelerated by projection-aware 3D feature learning methods. The superior performance and effectiveness of our LiDAR odometry architecture are demonstrated on KITTI odometry dataset. Our method outperforms all recent learning-based methods and even the geometry-based approach, LOAM with mapping optimization, on most sequences of KITTI odometry dataset.