In complex industrial processes, process fault detection and classification constitute an important task for reducing production costs and improving product quality. Most existing methods for fault classification assume that sufficient labeled data are available for training. However, label acquisition is costly and laborious in practice, whereas abundant unlabeled data are often available. To make effective use of a large amount of unlabeled data for fault classification, we propose in this article a new approach using semi-supervised deep generative models, allowing the complex relationship between high-dimensional process data and the process status to be modeled. In particular, to consider the temporal correlation and intervariable correlation in multivariate time series process data collected from multiple sensors, we propose two semi-supervised deep generative models incorporating convolutional neural networks. The proposed models are assessed on data from the Tennessee Eastman benchmark process. The results demonstrate the superior performances of the proposed models compared with competing methods.