Knowledge distillation (KD) has shown very promising capabilities in transferring learning representations from large models (teachers) to small models (students). However, as the capacity gap between students and teachers becomes larger, existing KD methods fail to achieve better results. Our work shows that the 'prior knowledge' is vital to KD, especially when applying large teachers. Particularly, we propose the dynamic prior knowledge (DPK), which integrates part of teacher's features as the prior knowledge before the feature distillation. This means that our method also takes the teacher's feature as input', not justtarget'. Besides, we dynamically adjust the ratio of the prior knowledge during the training phase according to the feature gap, thus guiding the student in an appropriate difficulty. To evaluate the proposed method, we conduct extensive experiments on two image classification benchmarks (i.e. CIFAR100 and ImageNet) and an object detection benchmark (\i.e. MS COCO). The results demonstrate the superiority of our method in performance under varying settings. Besides, our DPK makes the performance of the student model positively correlated with that of the teacher model, which means that we can further boost the accuracy of students by applying larger teachers. More importantly, DPK provides a fast solution in teacher model selection for any given model. Our codes will be publicly available for reproducibility.