As a basic task and key link of space situational awareness, space target recognition has become crucial in threat analysis, communication reconnaissance and electronic countermeasures. Using the fingerprint features carried by the electromagnetic signal to recognize is an effective method. Because traditional radiation source recognition technologies are difficult to obtain satisfactory expert features, automatic feature extraction methods based on deep learning have become popular. Although many deep learning schemes have been proposed, most of them are only used to solve the inter-class separable problem and ignore the intra-class compactness. In addition, the openness of the real space may invalidate the existing closed-set recognition methods. In order to solve the above problems, inspired by the application of prototype learning in image recognition, we propose a novel method for recognizing space radiation sources based on a multi-scale residual prototype learning network (MSRPLNet). The method can be used for both the closed- and open-set recognition of space radiation sources. Furthermore, we also design a joint decision algorithm for an open-set recognition task to identify unknown radiation sources. To verify the effectiveness and reliability of the proposed method, we built a set of satellite signal observation and receiving systems in a real external environment and collected eight Iridium signals. The experimental results show that the accuracy of our proposed method can reach 98.34% and 91.04% for the closed- and open-set recognition of eight Iridium targets, respectively. Compared to similar research works, our method has obvious advantages.