Few-Shot Class-Incremental Learning (FSCIL) models aim to incrementally learn new classes with scarce samples while preserving knowledge of old ones. Existing FSCIL methods usually fine-tune the entire backbone, leading to overfitting and hindering the potential to learn new classes. On the other hand, recent prompt-based CIL approaches alleviate forgetting by training prompts with sufficient data in each task. In this work, we propose a novel framework named Attention-aware Self-adaptive Prompt (ASP). ASP encourages task-invariant prompts to capture shared knowledge by reducing specific information from the attention aspect. Additionally, self-adaptive task-specific prompts in ASP provide specific information and transfer knowledge from old classes to new classes with an Information Bottleneck learning objective. In summary, ASP prevents overfitting on base task and does not require enormous data in few-shot incremental tasks. Extensive experiments on three benchmark datasets validate that ASP consistently outperforms state-of-the-art FSCIL and prompt-based CIL methods in term of both learning new classes and mitigating forgetting.