For the public and stakeholders, it is necessary to demonstrate airworthiness safety of AI-based avionics system in acceptable means of compliance, so as to solve problems of trustworthiness, uncertainty and explainability of civil aircraft avionics system caused by introducing artificial intelligence/machine learning technology. First of all, the classification and application status of AI-based avionics system are clarified, and the applicability of existing guidelines and standards are expounded. Then, based on the review of the current research progress, the implementation process and technical details of the certification framework for AI-based avionics system are summarized, including trustworthiness analysis, safety assessment, safety risk mitigation and certification/approval activities. Finally, it puts forward the requirements and implementation methods of the compliance verification of AI-based avionics system in each stage of the whole life cycle, and evaluates the impact of compliance verification on the existing airworthiness system. The study is significant to the design and certification of civil aircraft AI-based avionics system.