Mobile activity recognition focuses on inferring current user activities by leveraging sensory data available on today's sensor rich mobile phones. Supervised learning with static models has been applied pervasively for mobile activity recognition. In this paper, we propose a novel phone-based dynamic recognition framework with evolving data streams for activity recognition. The novel framework incorporates incremental and active learning for real-time recognition and adaptation in streaming settings. While stream evolves, we refine, enhance and personalise the learning model in order to accommodate the natural drift in a given datastream. Extensive experimental results using real activity recognition data have evidenced that the novel dynamic approach shows improved performance of recognising activities especially across different users.