Generative adversarial networks (GANs) have been shown to provide an effective way to model complex distributions and have obtained impressive results on various challenging tasks. However, typical GANs require fully-observed data during training. In this paper, we present a GAN-based framework for learning from complex, high-dimensional incomplete data. The proposed framework learns a complete data generator along with a mask generator that models the missing data distribution. We further demonstrate how to impute missing data by equipping our framework with an adversarially trained imputer. We evaluate the proposed framework using a series of experiments with several types of missing data processes under the missing completely at random assumption.