Most existing methods for audio classification assume that the vocabulary of audio classes to be classified is fixed. When novel (unseen) audio classes appear, audio classification systems need to be retrained with abundant labeled samples of all audio classes for recognizing base (initial) and novel audio classes. If novel audio classes continue to appear, the existing methods for audio classification will be inefficient and even infeasible. In this work, we propose a method for few-shot class-incremental audio classification, which can continually recognize novel audio classes without forgetting old ones. The framework of our method mainly consists of two parts: an embedding extractor and a classifier, and their constructions are decoupled. The embedding extractor is the backbone of a ResNet based network, which is frozen after construction by a training strategy using only samples of base audio classes. However, the classifier consisting of prototypes is expanded by a prototype adaptation network with few samples of novel audio classes in incremental sessions. Labeled support samples and unlabeled query samples are used to train the prototype adaptation network and update the classifier, since they are informative for audio classification. Three audio datasets, named NSynth-100, FSC-89 and LS-100 are built by choosing samples from audio corpora of NSynth, FSD-MIX-CLIP and LibriSpeech, respectively. Results show that our method exceeds baseline methods in average accuracy and performance dropping rate. In addition, it is competitive compared to baseline methods in computational complexity and memory requirement. The code for our method is given at https://github.com/vinceasvp/FCAC.