Numerous research efforts have been made to stabilize the training of the Generative Adversarial Networks (GANs), such as through regularization and architecture design. However, we identify the instability can also arise from the fragile balance at the early stage of adversarial learning. This paper proposes the CoopInit, a simple yet effective cooperative learning-based initialization strategy that can quickly learn a good starting point for GANs, with a very small computation overhead during training. The proposed algorithm consists of two learning stages: (i) Cooperative initialization stage: The discriminator of GAN is treated as an energy-based model (EBM) and is optimized via maximum likelihood estimation (MLE), with the help of the GAN's generator to provide synthetic data to approximate the learning gradients. The EBM also guides the MLE learning of the generator via MCMC teaching; (ii) Adversarial finalization stage: After a few iterations of initialization, the algorithm seamlessly transits to the regular mini-max adversarial training until convergence. The motivation is that the MLE-based initialization stage drives the model towards mode coverage, which is helpful in alleviating the issue of mode dropping during the adversarial learning stage. We demonstrate the effectiveness of the proposed approach on image generation and one-sided unpaired image-to-image translation tasks through extensive experiments.