Training deep models for semantic scene completion is challenging due to the sparse and incomplete input, a large quantity of objects of diverse scales as well as the inherent label noise for moving objects. To address the above-mentioned problems, we propose the following three solutions: 1) Redesigning the completion network. We design a novel completion network, which consists of several Multi-Path Blocks (MPBs) to aggregate multi-scale features and is free from the lossy downsampling operations. 2) Distilling rich knowledge from the multi-frame model. We design a novel knowledge distillation objective, dubbed Dense-to-Sparse Knowledge Distillation (DSKD). It transfers the dense, relation-based semantic knowledge from the multi-frame teacher to the single-frame student, significantly improving the representation learning of the single-frame model. 3) Completion label rectification. We propose a simple yet effective label rectification strategy, which uses off-the-shelf panoptic segmentation labels to remove the traces of dynamic objects in completion labels, greatly improving the performance of deep models especially for those moving objects. Extensive experiments are conducted in two public semantic scene completion benchmarks, i.e., SemanticKITTI and SemanticPOSS. Our SCPNet ranks 1st on SemanticKITTI semantic scene completion challenge and surpasses the competitive S3CNet by 7.2 mIoU. SCPNet also outperforms previous completion algorithms on the SemanticPOSS dataset. Besides, our method also achieves competitive results on SemanticKITTI semantic segmentation tasks, showing that knowledge learned in the scene completion is beneficial to the segmentation task.