Knowledge distillation aims to enhance the performance of a lightweight student model by exploiting the knowledge from a pre-trained cumbersome teacher model. However, in the traditional knowledge distillation, teacher predictions are only used to provide the supervisory signal for the last layer of the student model, which may result in those shallow student layers lacking accurate training guidance in the layer-by-layer back propagation and thus hinders effective knowledge transfer. To address this issue, we propose Deeply-Supervised Knowledge Distillation (DSKD), which fully utilizes class predictions and feature maps of the teacher model to supervise the training of shallow student layers. A loss-based weight allocation strategy is developed in DSKD to adaptively balance the learning process of each shallow layer, so as to further improve the student performance. Extensive experiments show that the performance of DSKD consistently exceeds state-of-the-art methods on various teacher-student models, confirming the effectiveness of our proposed method.