Pre-trained image-text models, like CLIP, have demonstrated the strong power of vision-language representation learned from a large scale of web-collected image-text data. In light of the well-learned visual features, there are works that transfer image representation to the video domain and achieve good results. However, adapting image-text pre-trained models to video-text pre-training (i.e., post-pretraining) has not demonstrated a significant advantage yet. In this paper, we tackle this challenge by raising and addressing two questions: 1) what are the factors hindering post-pretraining CLIP from improving performance on video-text tasks, and 2) how to mitigate the impact of these factors. Through a series of comparative experiments and analyses, we find that the data scale and domain gap between language sources have large impacts. By these observations, we propose an Omnisource Cross-modal Learning method equipped with a Video Proxy mechanism on the basis of CLIP, namely CLIP-ViP. Extensive results show that our approach improves the performance of CLIP on video-text retrieval by a large margin. Our model achieves state-of-the-art results on a variety of datasets, including MSR-VTT, DiDeMo, LSMDC, and ActivityNet. We release our code and pre-trained CLIP-ViP models at \url{https://github.com/microsoft/XPretrain/tree/main/CLIP-ViP}.