Point cloud salient object detection has attracted the attention of researchers in recent years. Since existing works do not fully utilize the geometry context of 3D objects, blurry boundaries are generated when segmenting objects with complex backgrounds. In this paper, we propose a geometry-aware 3D salient object detection network that explicitly clusters points into superpoints to enhance the geometric boundaries of objects, thereby segmenting complete objects with clear boundaries. Specifically, we first propose a simple yet effective superpoint partition module to cluster points into superpoints. In order to improve the quality of superpoints, we present a point cloud class-agnostic loss to learn discriminative point features for clustering superpoints from the object. After obtaining superpoints, we then propose a geometry enhancement module that utilizes superpoint-point attention to aggregate geometric information into point features for predicting the salient map of the object with clear boundaries. Extensive experiments show that our method achieves new state-of-the-art performance on the PCSOD dataset.