For distributed sensor systems using neural networks, each sub-network has a different electromagnetic environment, and these recognition accuracy is also different. In this paper, we propose a distributed sensor system using incremental learning to solve the problem of radio frequency fingerprint identification. First, the intelligent representation of the received signal is linearly fused into a four-channel image. Then, convolutional neural network is trained by using the existing data to obtain the preliminary model of the network, and decision fusion is used to solve the problem in the distributed system. Finally, using new data, instead of retraining the model, we employ incremental learning by fine-tuning the preliminary model. The proposed method can significantly reduce the training time and is adaptive to streaming data. Extensive experiments show that the proposed method is computationally efficient, and also has satisfactory recognition accuracy, especially at low signal-to-noise ratio (SNR) regime.