New classes of sounds constantly emerge with a few samples, making it challenging for models to adapt to dynamic acoustic environments. This challenge motivates us to address the new problem of few-shot class-incremental audio classification. This study aims to enable a model to continuously recognize new classes of sounds with a few training samples of new classes while remembering the learned ones. To this end, we propose a method to generate discriminative prototypes and use them to expand the model's classifier for recognizing sounds of new and learned classes. The model is first trained with a random episodic training strategy, and then its backbone is used to generate the prototypes. A dynamic relation projection module refines the prototypes to enhance their discriminability. Results on two datasets (derived from the corpora of Nsynth and FSD-MIX-CLIPS) show that the proposed method exceeds three state-of-the-art methods in average accuracy and performance dropping rate.