With the development of machine learning techniques, the attention of research has been moved from single-modal learning to multi-modal learning, as real-world data exist in the form of different modalities. However, multi-modal models often carry more information than single-modal models and they are usually applied in sensitive scenarios, such as medical report generation or disease identification. Compared with the existing membership inference against machine learning classifiers, we focus on the problem that the input and output of the multi-modal models are in different modalities, such as image captioning. This work studies the privacy leakage of multi-modal models through the lens of membership inference attack, a process of determining whether a data record involves in the model training process or not. To achieve this, we propose Multi-modal Models Membership Inference (M$^4$I) with two attack methods to infer the membership status, named metric-based (MB) M$^4$I and feature-based (FB) M$^4$I, respectively. More specifically, MB M$^4$I adopts similarity metrics while attacking to infer target data membership. FB M$^4$I uses a pre-trained shadow multi-modal feature extractor to achieve the purpose of data inference attack by comparing the similarities from extracted input and output features. Extensive experimental results show that both attack methods can achieve strong performances. Respectively, 72.5% and 94.83% of attack success rates on average can be obtained under unrestricted scenarios. Moreover, we evaluate multiple defense mechanisms against our attacks. The source code of M$^4$I attacks is publicly available at https://github.com/MultimodalMI/Multimodal-membership-inference.git.