The recent contrastive language-image pre-training (CLIP) model has shown great success in a wide range of image-level tasks, revealing remarkable ability for learning powerful visual representations with rich semantics. An open and worthwhile problem is efficiently adapting such a strong model to the video domain and designing a robust video anomaly detector. In this work, we propose VadCLIP, a new paradigm for weakly supervised video anomaly detection (WSVAD) by leveraging the frozen CLIP model directly without any pre-training and fine-tuning process. Unlike current works that directly feed extracted features into the weakly supervised classifier for frame-level binary classification, VadCLIP makes full use of fine-grained associations between vision and language on the strength of CLIP and involves dual branch. One branch simply utilizes visual features for coarse-grained binary classification, while the other fully leverages the fine-grained language-image alignment. With the benefit of dual branch, VadCLIP achieves both coarse-grained and fine-grained video anomaly detection by transferring pre-trained knowledge from CLIP to WSVAD task. We conduct extensive experiments on two commonly-used benchmarks, demonstrating that VadCLIP achieves the best performance on both coarse-grained and fine-grained WSVAD, surpassing the state-of-the-art methods by a large margin. Specifically, VadCLIP achieves 84.51% AP and 88.02% AUC on XD-Violence and UCF-Crime, respectively. Code and features are released at https://github.com/nwpu-zxr/VadCLIP.