Because of its important role in model compression, knowledge distillation has attracted much attention in the field of deep learning. However, the classical knowledge distillation algorithm only uses the information of a single sample, and neglects the importance of the relationship between samples, leading to its poor performance. To improve the efficiency and performance of knowledge transfer in knowledge distillation algorithm, this paper proposed a feature-space-embedding based contrastive knowledge distillation (FSECD) algorithm. The algorithm adopts efficient batch construction strategy, which embeds the student feature into the teacher feature space so that each student feature builds N contrastive pairs with N teacher features. In each pair, the teacher feature is optimized and fixed, while student feature is to be optimized and tunable. In the training process, the distance for positive pairs is narrowed and the distance for negative pairs is expanded, so that student model can perceive and learn the inter-sample relations of teacher model and realize the transfer of knowledge from teacher model to student model. Extensive experiments with different teacher/student architecture settings on CIFAR-100 and ImageNet datasets show that, FSECD algorithm achieves significant performance improvement without additional network structures and data when compared with other cutting-edge distillation methods, which further proves the importance of the inter-sample relations in knowledge distillation.