Recognizing 3-D objects in cluttered scenes is a challenging task. Common approaches find potential feature correspondences between a scene and candidate models by matching sampled local shape descriptors and select a few correspondences with the highest descriptor similarity to identify models that appear in the scene. However, real scans contain various nuisances, such as noise, occlusion, and featureless object regions. This makes selected correspondences have a certain portion of false positives, requiring adopting the time-consuming model verification many times to ensure accurate recognition. This paper proposes a 3-D object recognition approach with three key components. First, we construct a Signature of Geometric Centroids descriptor that is descriptive and robust, and apply it to find high-quality potential feature correspondences. Second, we measure geometric compatibility between a pair of potential correspondences based on isometry and three angle-preserving components. Third, we perform effective correspondence selection by using both descriptor similarity and compatibility with an auxiliary set of “less” potential correspondences. Experiments on publicly available data sets demonstrate the robustness and/or efficiency of the descriptor, selection approach, and recognition framework. Comparisons with the state-of-the-arts validate the superiority of our recognition approach, especially under challenging scenarios.