Traditional continual event detection relies on abundant labeled data for training, which is often impractical to obtain in real-world applications. In this paper, we introduce continual few-shot event detection (CFED), a more commonly encountered scenario when a substantial number of labeled samples are not accessible. The CFED task is challenging as it involves memorizing previous event types and learning new event types with few-shot samples. To mitigate these challenges, we propose a memory-based framework: Hierarchical Augmentation Network (HANet). To memorize previous event types with limited memory, we incorporate prototypical augmentation into the memory set. For the issue of learning new event types in few-shot scenarios, we propose a contrastive augmentation module for token representations. Despite comparing with previous state-of-the-art methods, we also conduct comparisons with ChatGPT. Experiment results demonstrate that our method significantly outperforms all of these methods in multiple continual few-shot event detection tasks.