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Real-world recognition system often encounters the challenge of unseen labels. To identify such unseen labels, multi-label zero-shot learning (ML-ZSL) focuses on transferring knowledge by a pre-trained textual label embedding (e.g., GloVe). However, such methods only exploit single-modal knowledge from a language model, while ignoring the rich semantic information inherent in image-text pairs. Instead, recently developed open-vocabulary (OV) based methods succeed in exploiting such information of image-text pairs in object detection, and achieve impressive performance. Inspired by the success of OV-based methods, we propose a novel open-vocabulary framework, named multi-modal knowledge transfer (MKT), for multi-label classification. Specifically, our method exploits multi-modal knowledge of image-text pairs based on a vision and language pre-training (VLP) model. To facilitate transferring the image-text matching ability of VLP model, knowledge distillation is employed to guarantee the consistency of image and label embeddings, along with prompt tuning to further update the label embeddings. To further enable the recognition of multiple objects, a simple but effective two-stream module is developed to capture both local and global features. Extensive experimental results show that our method significantly outperforms state-of-the-art methods on public benchmark datasets. The source code is available at https://github.com/sunanhe/MKT.