In open-domain dialogue systems, generative approaches have attracted much attention for response generation. However, existing methods are heavily plagued by generating safe responses and unnatural responses. To alleviate these two problems, we propose a novel framework named Dual Adversarial Learning(DAL) for high-quality response generation. DAL innovatively utilizes the duality between query generation and response generation to avoid safe responses and increase the diversity of the generated responses. Additionally, DAL uses adversarial learning to mimic human judges and guides the system to generate natural responses. Experimental results demonstrate that DAL effectively improves both diversity and overall quality of the generated responses. DAL outperforms state-of-the-art methods regarding automatic metrics and human evaluations.