Although well-trained deep neural networks have shown remarkable performance on numerous tasks, they rapidly forget what they have learned as soon as they begin to learn with additional data with the previous data stop being provided. In this paper, we introduce a novel algorithm, Incremental Class Learning with Attribute Sharing (ICLAS), for incremental class learning with deep neural networks. As one of its component, we also introduce a generative model, incGAN, which can generate images with increased variety compared with the training data. Under challenging environment of data deficiency, ICLAS incrementally trains classification and the generation networks. Since ICLAS trains both networks, our algorithm can perform multiple times of incremental class learning. The experiments on MNIST dataset demonstrate the advantages of our algorithm.