In this paper, we present a novel end-to-end learning-based LiDAR relocalization framework, termed PointLoc, which infers 6-DoF poses directly using only a single point cloud as input, without requiring a pre-built map. Compared to RGB image-based relocalization, LiDAR frames can provide rich and robust geometric information about a scene. However, LiDAR point clouds are unordered and unstructured making it difficult to apply traditional deep learning regression models for this task. We address this issue by proposing a novel PointNet-style architecture with self-attention to efficiently estimate 6-DoF poses from 360{deg} LiDAR input frames.Extensive experiments on recently released challenging Oxford Radar RobotCar dataset and real-world robot experiments demonstrate that the proposedmethod can achieve accurate relocalization performance.