Inverse design has long been an efficient and powerful design tool in the aircraft industry. In this paper, a novel inverse design method for supercritical airfoils is proposed based on generative models in deep learning. A Conditional Variational AutoEncoder (CVAE) and an integrated generative network CVAE-GAN that combines the CVAE with the Wasserstein Generative Adversarial Networks (WGAN), are conducted as generative models. They are used to generate target wall Mach distributions for the inverse design that matches specified features, such as locations of suction peak, shock and aft loading. Qualitative and quantitative results show that both adopted generative models can generate diverse and realistic wall Mach number distributions satisfying the given features. The CVAE-GAN model outperforms the CVAE model and achieves better reconstruction accuracies for all the samples in the dataset. Furthermore, a deep neural network for nonlinear mapping is adopted to obtain the airfoil shape corresponding to the target wall Mach number distribution. The performances of the designed deep neural network are fully demonstrated and a smoothness measurement is proposed to quantify small oscillations in the airfoil surface, proving the authenticity and accuracy of the generated airfoil shapes.