Dominant dual-encoder models enable efficient imagetext retrieval but suffer from limited accuracy, while the cross-encoder models offer higher accuracy at the expense of efficiency. Distilling cross-modality matching knowledge from cross-encoder to dual-encoder provides a natural approach to harness their strengths. Thus, we investigate the following valuable question: how to make crossencoder a good teacher for dual-encoder? Our findings are threefold: (1) Cross-modal similarity score distribution of cross-encoder is more concentrated, while the result of dual-encoder is nearly normal, making vanilla logit distillation less effective. However, ranking distillation remains practical, as it is not affected by the score distribution. (2) Only the relative order between hard negatives conveys valid knowledge, while the order information between easy negatives has little significance. (3) Maintaining the coordination between distillation loss and dual-encoder training loss is beneficial for knowledge transfer. Based on these findings, we propose a novel Contrastive Partial Ranking Distillation (CPRD) method, which implements the objective of mimicking relative order between hard negative samples with contrastive learning. This approach coordinates with the training of the dual-encoder, effectively transferring valid knowledge from the cross-encoder to the dualencoder. Extensive experiments on image-text retrieval and ranking tasks show that our method surpasses other distillation methods and significantly improves the accuracy of dual-encoder.