Correspondence-based six-degree-of-freedom (6-DoF) pose estimation remains a mainstream solution for 3D point cloud registration. However, the heavy outliers pose great challenges to this problem. In this paper, we propose a random sample consensus (RANSAC) variant based on sampling locally and hypothesis globally (SLHG) for 6-DoF pose estimation and 3D point cloud registration. The key novelties are efficient sampling by guiding the sampling process locally and accurate pose estimation by generating hypotheses with global information. SLHG first generates a correspondence subset via compatibility clustering on the initial set. Second, locally guided graph sampling is performed. Third, 6-DoF hypotheses are generated by incorporating global information with a voting scheme. The best hypothesis serves as the estimation result by repeating the second and third steps. Extensive experiments on four popular datasets and comparisons with state-of-the-art methods confirm that: SLHG manages to 1) achieve accurate registrations with a few iterations, and 2) yield better accuracy performance than most competitors.