Open-domain conversation is one of the most challenging artificial intelligence problems, which involves language understanding, reasoning, and the utilization of common sense knowledge. The goal of this paper is to further improve the response generation, using personalization criteria. We propose a novel method called PRGDDA (Personalized Response Generation by Dual-learning based Domain Adaptation) which is a personalized response generation model based on theories of domain adaptation and dual learning. During the training procedure, PRGDDA first learns the human responding style from large general data (without user-specific information), and then fine-tunes the model on a small size of personalized data to generate personalized conversations with a dual learning mechanism. We conduct experiments to verify the effectiveness of the proposed model on two real-world datasets in both English and Chinese. Experimental results show that our model can generate better personalized responses for different users.