Test-time adaptation using vision-language model (such as CLIP) to quickly adjust to distributional shifts of downstream tasks has shown great potential. Despite significant progress, existing methods are still limited to single-task test-time adaptation scenarios and have not effectively explored the issue of multi-task adaptation. To address this practical problem, we propose a novel Hierarchical Knowledge Prompt Tuning (HKPT) method, which achieves joint adaptation to multiple target domains by mining more comprehensive source domain discriminative knowledge and hierarchically modeling task-specific and task-shared knowledge. Specifically, HKPT constructs a CLIP prompt distillation framework that utilizes the broader source domain knowledge of large teacher CLIP to guide prompt tuning for lightweight student CLIP from multiple views during testing. Meanwhile, HKPT establishes task-specific dual dynamic knowledge graph to capture fine-grained contextual knowledge from continuous test data. And to fully exploit the complementarity among multiple target tasks, HKPT employs an adaptive task grouping strategy for achieving inter-task knowledge sharing. Furthermore, HKPT can seamlessly transfer to basic single-task test-time adaptation scenarios while maintaining robust performance. Extensive experimental results in both multi-task and single-task test-time adaptation settings demonstrate that our HKPT significantly outperforms state-of-the-art methods.