Recently, transformation-based self-supervised learning has been applied to generative adversarial networks (GANs) to mitigate the catastrophic forgetting problem of discriminator by learning stable representations. However, the separate self-supervised tasks in existing self-supervised GANs cause an inconsistent goal with generative modeling due to the learning of the generator from their generator distribution-agnostic classifiers. To address this issue, we propose a novel self-supervised GANs framework with label augmentation, i.e., augmenting the GAN labels (real or fake) with the self-supervised pseudo-labels. In particular, the discriminator and the self-supervised classifier are unified to learn a single task that predicts the augmented label such that the discriminator/classifier is aware of the generator distribution, while the generator tries to confuse the discriminator/classifier by optimizing the discrepancy between the transformed real and generated distributions. Theoretically, we prove that the generator, at the equilibrium point, converges to replicate the data distribution. Empirically, we demonstrate that the proposed method significantly outperforms competitive baselines on both generative modeling and representation learning across benchmark datasets.