Conventional domain adaptation typically transfers knowledge from a source domain to a stationary target domain. However, in many real-world cases, target data usually emerge sequentially and have continuously evolving distributions. Restoring and adapting to such target data results in escalating computational and resource consumption over time. Hence, it is vital to devise algorithms to address the evolving domain adaptation (EDA) problem, \emph{i.e.,} adapting models to evolving target domains without access to historic target domains. To achieve this goal, we propose a simple yet effective approach, termed progressive conservative adaptation (PCAda). To manage new target data that diverges from previous distributions, we fine-tune the classifier head based on the progressively updated class prototypes. Moreover, as adjusting to the most recent target domain can interfere with the features learned from previous target domains, we develop a conservative sparse attention mechanism. This mechanism restricts feature adaptation within essential dimensions, thus easing the inference related to historical knowledge. The proposed PCAda is implemented with a meta-learning framework, which achieves the fast adaptation of the classifier with the help of the progressively updated class prototypes in the inner loop and learns a generalized feature without severely interfering with the historic knowledge via the conservative sparse attention in the outer loop. Experiments on Rotated MNIST, Caltran, and Portraits datasets demonstrate the effectiveness of our method.