Since open social platforms allow for a large and continuous flow of unverified information, rumors can emerge unexpectedly and spread quickly. However, existing rumor detection (RD) models often assume the same training and testing distributions and can not cope with the continuously changing social network environment. This paper proposed a Continual Prompt-Tuning RD (CPT-RD) framework, which avoids catastrophic forgetting (CF) of upstream tasks during sequential task learning and enables bidirectional knowledge transfer between domain tasks. Specifically, we propose the following strategies: (a) Our design explicitly decouples shared and domain-specific knowledge, thus reducing the interference among different domains during optimization; (b) Several technologies aim to transfer knowledge of upstream tasks to deal with emergencies; (c) A task-conditioned prompt-wise hypernetwork (TPHNet) is used to consolidate past domains. In addition, CPT-RD avoids CF without the necessity of a rehearsal buffer. Finally, CPT-RD is evaluated on English and Chinese RD datasets and is effective and efficient compared to prior state-of-the-art methods.