Much research has focused on classification within a closed set of emitters, while emitters outside this closed set are misclassified. This paper proposes an open-set recognition model based on prototypical networks and extreme value theory to solve the problem of specific emitter identification in open-set scenes and further improve the recognition accuracy and robustness. Firstly, a one-dimensional convolutional neural network was designed for recognizing I/Q signals, and a squeeze-and-excitation block with an attention mechanism was added to the network to increase the weights of the feature channels with high efficiency. Meanwhile, the recognition was improved by group convolution and channel shuffle. Then, the network was trained with the joint loss function based on prototype learning to complete the separation of intra-class signals and the aggregation of inter-class signals in the feature space. After the training, the Weibull model was fitted for pre-defined classes by incorporating the extreme value theory. Finally, the classification results were obtained according to the known classes and the Weibull model, effectively completing the open-set recognition. The simulation results showed that the proposed model had a higher recognition performance and robustness compared with other classical models for signals collected from five ZigBee and ten USRP 310 devices.