With the rapid development of neural network and other technologies, artificial intelligence has been widely applied in safety-critical or mission-critical systems, such as autopilot systems, disease diagnosis systems, and malware detection systems. Due to the lack of a comprehensive and in-depth understanding of artificial intelligence software systems, some errors with serious consequences occur frequently. The functional attributes and non-functional attributes of artificial intelligence software systems are proposed to enhance the adequate understanding and quality assurance of artificial intelligence software systems. After investigation, a large number of researchers are devoted to the study of functional attributes, but people are paying more and more attention to the non-functional attributes of artificial intelligence software systems. This paper investigates 138 papers in related fields, systematically combs the existing research results from the aspects of attribute necessity, attribute definition, attribute examples, and common quality assurance methods, and summarizes the research work on non-functional attributes of artificial intelligence software systems. At the same time, a summary and relationship analysis are presented on the non-functional attributes of artificial intelligence software systems. The open source tools that can be used in the research of artificial intelligence software system are surveyed. Finally, the thoughts on potential future research directions and challenges are summarized on non-functional attributes of artificial intelligence software systems, which, hopefully, will provide references for researchers interested in the related directions.