There is a widespread demand for Artificial Intelligence (AI) software, specifically Machine Learning (ML). It is getting increasingly popular and being adopted in various applications we use daily. AI-based software quality is different from traditional software quality because it generally addresses distinct and more complex kinds of problems. With the fast advance of AI technologies and related techniques, how to build high-quality AI-based software becomes a very prominent subject. This paper aims at investigating the state of the art on software quality (SQ) for AI-based systems and identifying quality attributes, applied models, challenges, and practices that are reported in the literature. We carried out a systematic literature review (SLR) from 1988 to 2020 to (i) analyze and understand related primary studies and (ii) synthesize limitations and open challenges to drive future research. Our study provides a road map for researchers to understand quality challenges, attributes, and practices in the context of software quality for AI-based software better. From the empirical evidence that we have gathered by this SLR, we suggest future work on this topic be structured under three categories which are Definition/Specification, Design/Evaluation, and Process/Socio-technical.