This Point cloud segmentation is a fundamental yet challenging step in point cloud processing, with wide applications in object recognition, 3D reconstruction and scene understanding. However, the traditional point cloud segmentation methods are susceptible to data noise and suffer from low segmentation accuracy and blurred boundaries. To this end, we propose a supervoxel-based object segmentation method which consists of three stages. First, a boundary-refined supervoxel segmentation method is proposed to generate the supervoxels as the processing elements, which can guarantee the accuracy of object segmentation boundaries and improve processing efficiency. Second, an improved region growing method is proposed to obtain a series of facets using a novel seed selection criterion. Finally, a convexity-based merging method is proposed to achieve complete objects by judging the concavity between adjacent facets. The method is experimented on synthetic datasets and public datasets. The visualization and quantitative comparison results show that our method outperforms the reference methods in terms of segmentation accuracy and completeness.