In recent years, artificial intelligence (AI) has rapidly developed. AI systems have penetrated people’s lives and become an indispensable part. However, these systems require a large amount of data to train models, and data disturbances will affect their results. Furthermore, as the business becomes diversified, and the scale gets complex, the trustworthiness of AI systems has attracted wide attention. Firstly, based on the trustworthiness attributes proposed by different organizations and scholars, this study introduces nine trustworthiness attributes of AI systems. Next, in terms of the data, model, and result trustworthiness, the study discusses methods for measuring the data, model, and result trustworthiness of existing AI systems and designs an evidence collection method of AI trustworthiness. Then, it summarizes the trustworthiness measurement theory and methods of AI systems. In addition, combined with attribute-based software trustworthiness measurement methods and blockchain technologies, the study establishes a trustworthiness measurement framework for AI systems, which includes methods of trustworthiness attribute decomposition and evidence acquisition, the federation trustworthiness measurement model, and the blockchain-based trustworthiness measurement structure of AI systems. Finally, it describes the opportunities and challenges of trustworthiness measurement technologies for AI systems.