Model inversion (MI) attacks pose significant privacy risks by reconstructing private training data from trained neural networks. While prior works have focused on conventional unimodal DNNs, the vulnerability of vision-language models (VLMs) remains underexplored. In this paper, we conduct the first study to understand VLMs' vulnerability in leaking private visual training data. To tailored for VLMs' token-based generative nature, we propose a suite of novel token-based and sequence-based model inversion strategies. Particularly, we propose Token-based Model Inversion (TMI), Convergent Token-based Model Inversion (TMI-C), Sequence-based Model Inversion (SMI), and Sequence-based Model Inversion with Adaptive Token Weighting (SMI-AW). Through extensive experiments and user study on three state-of-the-art VLMs and multiple datasets, we demonstrate, for the first time, that VLMs are susceptible to training data leakage. The experiments show that our proposed sequence-based methods, particularly SMI-AW combined with a logit-maximization loss based on vocabulary representation, can achieve competitive reconstruction and outperform token-based methods in attack accuracy and visual similarity. Importantly, human evaluation of the reconstructed images yields an attack accuracy of 75.31\%, underscoring the severity of model inversion threats in VLMs. Notably we also demonstrate inversion attacks on the publicly released VLMs. Our study reveals the privacy vulnerability of VLMs as they become increasingly popular across many applications such as healthcare and finance.