As one of the information industry’s future development directions, the Internet of Things (IoT) has been widely used. In order to reduce the pressure on the network caused by the long distance between the processing platform and the terminal, edge computing provides a new paradigm for IoT applications. In many scenarios, the IoT devices are distributed in remote areas or extreme terrain and cannot be accessed directly through the terrestrial network, and data transmission can only be achieved via satellite. However, traditional satellites are highly customized, and on-board resources are designed for specific applications rather than universal computing. Therefore, we propose to transform the traditional satellite into a space edge computing node. It can dynamically load software in orbit, flexibly share on-board resources, and provide services coordinated with the cloud. The corresponding hardware structure and software architecture of the satellite is presented. Through the modeling analysis and simulation experiments of the application scenarios, the results show that the space edge computing system takes less time and consumes less energy than the traditional satellite constellation. The quality of service is mainly related to the number of satellites, satellite performance, and task offloading strategy.