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Generative adversarial networks (GANs) have been a popular deep generative model for real-world applications. Despite many recent efforts on GANs that have been contributed, mode collapse and instability of GANs are still open problems caused by their adversarial optimization difficulties. In this paper, motivated by the cooperative co-evolutionary algorithm, we propose a Cooperative Dual Evolution based Generative Adversarial Network (CDE-GAN) to circumvent these drawbacks. In essence, CDE-GAN incorporates dual evolution with respect to the generator(s) and discriminators into a unified evolutionary adversarial framework to conduct effective adversarial multi-objective optimization. Thus it exploits the complementary properties and injects dual mutation diversity into training to steadily diversify the estimated density in capturing multi-modes and improve generative performance. Specifically, CDE-GAN decomposes the complex adversarial optimization problem into two subproblems (generation and discrimination), and each subproblem is solved with a separated subpopulation (E-Generator} and E-Discriminators), evolved by its own evolutionary algorithm. Additionally, we further propose a Soft Mechanism to balance the trade-off between E-Generators and E-Discriminators to conduct steady training for CDE-GAN. Extensive experiments on one synthetic dataset and three real-world benchmark image datasets demonstrate that the proposed CDE-GAN achieves a competitive and superior performance in generating good quality and diverse samples over baselines. The code and more generated results are available at our project homepage: https://shiming-chen.github.io/CDE-GAN-website/CDE-GAN.html.