Video retrieval is becoming increasingly important owing to the rapid emergence of videos on the Internet. The dominant paradigm for video retrieval learns video-text representations by pushing the distance between the similarity of positive pairs and that of negative pairs apart from a fixed margin. However, negative pairs used for training are sampled randomly, which indicates that the semantics between negative pairs may be related or even equivalent, while most methods still enforce dissimilar representations to decrease their similarity. This phenomenon leads to inaccurate supervision and poor performance in learning video-text representations. While most video retrieval methods overlook that phenomenon, we propose an adaptive margin changed with the distance between positive and negative pairs to solve the aforementioned issue. First, we design the calculation framework of the adaptive margin, including the method of distance measurement and the function between the distance and the margin. Then, we explore a novel implementation called "Cross-Modal Generalized Self-Distillation" (CMGSD), which can be built on the top of most video retrieval models with few modifications. Notably, CMGSD adds few computational overheads at train time and adds no computational overhead at test time. Experimental results on three widely used datasets demonstrate that the proposed method can yield significantly better performance than the corresponding backbone model, and it outperforms state-of-the-art methods by a large margin.