Deep Neural Networks (DNNs) are known to be susceptible to adversarial attacks. Previous researches mainly focus on improving adversarial robustness in the fully supervised setting, leaving the challenging domain of zero-shot adversarial robustness an open question. In this work, we investigate this domain by leveraging the recent advances in large vision-language models, such as CLIP, to introduce zero-shot adversarial robustness to DNNs. We propose LAAT, a Language-driven, Anchor-based Adversarial Training strategy. LAAT utilizes the features of a text encoder for each category as fixed anchors (normalized feature embeddings) for each category, which are then employed for adversarial training. By leveraging the semantic consistency of the text encoders, LAAT aims to enhance the adversarial robustness of the image model on novel categories. However, naively using text encoders leads to poor results. Through analysis, we identified the issue to be the high cosine similarity between text encoders. We then design an expansion algorithm and an alignment cross-entropy loss to alleviate the problem. Our experimental results demonstrated that LAAT significantly improves zero-shot adversarial robustness over state-of-the-art methods. LAAT has the potential to enhance adversarial robustness by large-scale multimodal models, especially when labeled data is unavailable during training.