The lack of fine-grained 3D shape seg-mentation data is the main obstacle to developing learning-based 3D segmentation techniques. We pro-pose an effective semi-supervised method for learning 3D segmentations from a few labeled 3D shapes and a large amount of unlabeled 3D data. For the unlabeled data, we present a novel multilevel consistency loss to enforce consistency of network predictions between perturbed copies of a 3D shape at multiple levels: point level, part level, and hierarchical level. For the labeled data, we develop a simple yet effective part substitution scheme to augment the labeled 3D shapes with more structural variations to enhance training. Our method has been extensively validated on the task of 3D object semantic segmentation on PartNet and ShapeNetPart, and indoor scene semantic segmentation on ScanNet. It exhibits superior performance to existing semi-supervised and unsupervised pre-training 3D approaches.