Point cloud registration is a fundamental task in high level three dimensional applications. Noise, uneven point density and varying point cloud resolutions are the three main challenges for point cloud registration. In this paper, we design a robust and compact local surface descriptor called Local Surface Angles Histogram (LSAH) and propose an effectively coarse to fine algorithm for point cloud registration. The LSAH descriptor is formed by concatenating five normalized sub-histograms into one histogram. The five sub-histograms are created by accumulating a different type of angle from a local surface patch respectively. The experimental results show that our LSAH is more robust to uneven point density and point cloud resolutions than four state-of-the-art local descriptors in terms of feature matching. Moreover, we tested our LSAH based coarse to fine algorithm for point cloud registration. The experimental results demonstrate that our algorithm is robust and efficient as well.