We propose a novel neural network model that aims to generate diverse and human-like natural language questions. Our model not only directly captures the variability in possible questions by using a latent variable, but also generates certain types of questions by introducing an additional observed variable. We deploy our model in the generative adversarial network (GAN) framework and modify the discriminator which not only allows evaluating the question authenticity, but predicts the question type. Our model is trained and evaluated on a question-answering dataset SQuAD, and the experimental results shown the proposed model is able to generate diverse and readable questions with the specific attribute.