Video-language models suffer from forgetting old/learned knowledge when trained with streaming data. In this work, we thus propose a continual video-language modeling (CVLM) setting, where models are supposed to be sequentially trained on five widely-used video-text datasets with different data distributions. Although most of existing continual learning methods have achieved great success by exploiting extra information (e.g., memory data of past tasks) or dynamically extended networks, they cause enormous resource consumption when transferred to our CVLM setting. To overcome the challenges (i.e., catastrophic forgetting and heavy resource consumption) in CVLM, we propose a novel cross-modal MoCo-based model with bidirectional momentum update (BMU), termed BMU-MoCo. Concretely, our BMU-MoCo has two core designs: (1) Different from the conventional MoCo, we apply the momentum update to not only momentum encoders but also encoders (i.e., bidirectional) at each training step, which enables the model to review the learned knowledge retained in the momentum encoders. (2) To further enhance our BMU-MoCo by utilizing earlier knowledge, we additionally maintain a pair of global momentum encoders (only initialized at the very beginning) with the same BMU strategy. Extensive results show that our BMU-MoCo remarkably outperforms recent competitors w.r.t. video-text retrieval performance and forgetting rate, even without using any extra data or dynamic networks.