The intelligent autonomy and stable on-orbit operation capabilities of spacecraft are crucial to enhancing the success rate of space missions. Software self-adaptive evolution technology is an essential approach to achieving this goal and has become a research hotspot in the field of software engineering. This study first provides an overview of the research status and existing issues in the self-adaptive evolution of spacecraft control software. Then, in response to the openness of the spacecraft on-orbit operating environment, the limited computing resources of the host, and the high real-time response requirements of flight missions, an on-orbit self-adaptive and trustworthy evolution framework for spacecraft control software, termed MAPE-KV (monitor-analyze-plan-execute over knowledge and verification), is proposed. In addition, under the guidance of this framework, the application logic, self-adaptive control logic, trustworthiness assurance logic, and supporting knowledge base for spacecraft software are designed. Finally, the effectiveness of the proposed framework is validated through two typical scenarios: unexpected failures and service changes. Simulation results demonstrate that the proposed method can effectively address the challenges posed by unexpected events during the operation of spaceborne software.