Knowledge distillation is widely used in pre-trained language model compression, which can transfer knowledge from a cumbersome model to a lightweight one. Though knowledge distillation based model compression has achieved promising performance, we observe that explanations between the teacher model and the student model are not consistent. We argue that the student model should study not only the predictions of the teacher model but also the internal reasoning process. To this end, we propose Explanation Guided Knowledge Distillation (EGKD) in this article, which utilizes explanations to represent the thinking process and improve knowledge distillation. To obtain explanations in our distillation framework, we select three typical explanation methods rooted in different mechanisms, namely gradient-based, perturbation-based, and feature selection methods. Then, to improve computational efficiency, we propose different optimization strategies to utilize the explanations obtained by these three different explanation methods, which could provide the student model with better learning guidance. Experimental results on GLUE demonstrate that leveraging explanations can improve the performance of the student model. Moreover, our EGKD could also be applied to model compression with different architectures.