Due to limited storage, edge devices in the Internet of Things (IoT) usually retain data for a limited time period. In real production processes, the equipment conditions change over time, often generating new classes of fault data or images. This class increment can cause catastrophic forgetting when the model is trained locally. Based on the partial catastrophic forgetting of class increment on a single edge, catastrophic forgetting will spread with the collaborative optimization of cloud and edge. To address the above problems, a federated class incremental learning method based on stable feature prototypes is proposed. A class sample memory is established at the edge to store representative samples of the class. A feature network update strategy based on the replay paradigm is designed. A weighted aggregation strategy based on feature prototypes in a unified feature space is designed in the cloud. The feature space is stably optimized in the federated framework to realize the federated update of class knowledge. Experiments on CIFAR10 and Mini-ImageNet, which are commonly used datasets for class increment, demonstrate that the proposed method can effectively alleviate catastrophic forgetting.