Instance segmentation is an important pre-processing task in numerous real-world applications, such as robotics, autonomous vehicles, and human-computer interaction. Compared with the rapid development of deep learning for two-dimensional (2D) image tasks, deep learning-based instance segmentation of 3D point cloud still has a lot of room for development. In particular, distinguishing a large number of occluded objects of the same class is a highly challenging problem, which is seen in a robotic bin-picking. In a usual bin-picking scene, many identical objects are stacked together and the model of the objects is known. Thus, the semantic information can be ignored; instead, the focus in the bin-picking is put on the segmentation of instances. Based on this task requirement, we propose a Fast Point Cloud Clustering (FPCC) for instance segmentation of bin-picking scene. FPCC includes a network named FPCC-Net and a fast clustering algorithm. FPCC-net has two subnets, one for inferring the geometric centers for clustering and the other for describing features of each point. FPCC-Net extracts features of each point and infers geometric center points of each instance simultaneously. After that, the proposed clustering algorithm clusters the remaining points to the closest geometric center in feature embedding space. Experiments show that FPCC also surpasses the existing works in bin-picking scenes and is more computationally efficient. Our code and data are available at https://github.com/xyjbaal/FPCC.