Multi-label classification (MLC) is pervasive in real-world applications. Conventional MLC algorithms assume that enough ground truth labels are available for training a classifier. While in reality, obtaining ground truth labels is expensive and time-consuming. In the field of data mining, it is more efficient to use crowdsourcing for label collection. In this setting, an MLC algorithm needs to deal with the noisiness of the crowdsourced labels as well as the remaining massive unlabeled data. In this paper, we propose a deep generative model to describe the label generation process for this semi-supervised multi-label learning problem. Although deep generative models are widely used for MLC problems, no previous work could address the noisy crowdsourced multi-labels and unlabeled data simultaneously. To address this challenging problem, our novel generative model incorporates latent variables to describe the labeled/unlabeled data as well as the labeling process of crowdsourcing. We introduce an efficient sequential inference model to approximate the model posterior and infer the ground truth labels. Our experimental results on various scales of datasets demonstrate the effectiveness of our proposed model. It performs favorably against four state-of-the-art deep generative models.