Activity of daily living is an important indicator of the health status and functional capabilities of an individual. Activity recognition, which aims at understanding the behavioral patterns of people, has increasingly received attention in recent years. However, there are still a number of challenges confronting the task. First, labelling training data is expensive and time-consuming, leading to limited availability of annotations. Secondly, activities performed by individuals have considerable variability, which renders the generally used supervised learning with a fixed label set unsuitable. To address these issues, we propose a dynamic active learning-based activity recognition method in this work. Different from traditional active learning methods which select samples based on a fixed label set, the proposed method not only selects informative samples from known classes, but also dynamically identifies new activities which are not included in the predefined label set. Starting with a classifier that has access to a limited number of labelled samples, we iteratively extend the training set with informative labels by fully considering the uncertainty, diversity and representativeness of samples, based on which better-informed classifiers can be trained, further reducing the annotation cost. We evaluate the proposed method on two synthetic datasets and two existing benchmark datasets. Experimental results demonstrate that our method not only boosts the activity recognition performance with considerably reduced annotation cost, but also enables adaptive daily activity analysis allowing the presence and detection of novel activities and patterns.