Nowadays, with the rapid development of data collection sources and feature extraction methods, multi-view data are getting easy to obtain and have received increasing research attention in recent years, among which, multi-view clustering (MVC) forms a mainstream research direction and is widely used in data analysis. However, existing MVC methods mainly assume that each sample appears in all the views, without considering the incomplete view case due to data corruption, sensor failure, equipment malfunction, etc. In this study, we design and build a generative partial multi-view clustering model, named as GP-MVC, to address the incomplete multi-view problem by explicitly generating the data of missing views. The main idea of GP-MVC lies at two-fold. First, multi-view encoder networks are trained to learn common low-dimensional representations, followed by a clustering layer to capture the consistent cluster structure across multiple views. Second, view-specific generative adversarial networks are developed to generate the missing data of one view conditioning on the shared representation given by other views. These two steps could be promoted mutually, where learning common representations facilitates data imputation and the generated data could further explores the view consistency. Moreover, an weighted adaptive fusion scheme is implemented to exploit the complementary information among different views. Experimental results on four benchmark datasets are provided to show the effectiveness of the proposed GP-MVC over the state-of-the-art methods.