Generative Adversarial Networks (GANs) with high computation costs, e.g., BigGAN and StyleGAN2, have achieved remarkable results in synthesizing high resolution and diverse images with high fidelity from random noises. Reducing the computation cost of GANs while keeping generating photo-realistic images is an urgent and challenging field for their broad applications on computational resource-limited devices. In this work, we propose a novel yet simple Discriminator Guided Learning approach for compressing vanilla GAN, dubbed DGL-GAN. Motivated by the phenomenon that the teacher discriminator may contain some meaningful information, we transfer the knowledge merely from the teacher discriminator via the adversarial function. We show DGL-GAN is valid since empirically, learning from the teacher discriminator could facilitate the performance of student GANs, verified by extensive experimental findings. Furthermore, we propose a two-stage training strategy for training DGL-GAN, which can largely stabilize its training process and achieve superior performance when we apply DGL-GAN to compress the two most representative large-scale vanilla GANs, i.e., StyleGAN2 and BigGAN. Experiments show that DGL-GAN achieves state-of-the-art (SOTA) results on both StyleGAN2 (FID 2.92 on FFHQ with nearly 1/3 parameters of StyleGAN2) and BigGAN (IS 93.29 and FID 9.92 on ImageNet with nearly 1/4 parameters of BigGAN) and also outperforms several existing vanilla GAN compression techniques. Moreover, DGL-GAN is also effective in boosting the performance of original uncompressed GANs, original uncompressed StyleGAN2 boosted with DGL-GAN achieves FID 2.65 on FFHQ, which achieves a new state-of-the-art performance. Code and models are available at https://github.com/yuesongtian/DGL-GAN.