While end-to-end neural conversation models have led to promising advances in reducing hand-crafted features and errors induced by the traditional complex system architecture, they typically require an enormous amount of data due to the lack of modularity. Previous studies adopted a hybrid approach with knowledge-based components either to abstract out domain-specific information or to augment data to cover more diverse patterns. On the contrary, we propose to directly address the problem using recent developments in the space of continual learning for neural models. Specifically, we adopt a domain-independent neural conversational model and introduce a novel neural continual learning algorithm that allows a conversational agent to accumulate skills across different tasks in a data-efficient way. To the best of our knowledge, this is the first work that applies continual learning to conversation systems. We verified the efficacy of our method through a conversational skill transfer from either synthetic dialogs or human-human dialogs to human-computer conversations in a customer support domain.