Intent detection is at the core of task-oriented dialogue systems. Existing intent detection systems are typically trained with a large amount of data over a predefined set of intent classes. However, newly emerged intents in multiple domains are commonplace in the real world. And it is time-consuming and impractical for dialogue systems to re-collect enough annotated data and re-train the model. These limitations call for an intent detection system that could continually recognize new intents with very few labeled examples. In this work, we study the Continual Few-shot Intent Detection (CFID) problem and construct a benchmark consisting of nine tasks with multiple domains and imbalanced classes. To address the key challenges of (a) catastrophic forgetting during continuous learning and (b) negative knowledge transfer across tasks, we propose the Prefix-guided Lightweight Encoder (PLE) with three auxiliary strategies, namely Pseudo Samples Replay (PSR), Teacher Knowledge Transfer (TKT) and Dynamic Weighting Replay (DWR). Extensive experiments demonstrate the effectiveness and efficiency of our method in preventing catastrophic forgetting and encouraging positive knowledge transfer across tasks.