© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.Context: In the last two decades, open-source software (OSS) has gained increasing attention due to its voluntary supporters, growing community, and ease of accessibility in cloud repositories. Standardization in OSS quality is of vital importance as a communication vehicle for stakeholders in identifying and selecting high-quality products. Thus, meta-models help to define a standardized language and enable to propose quality models that can be used to perform comparable measurements. Objective: Considering the lack of a comprehensive meta-model of OSS quality in the literature, there appears a need to see a more complete picture of OSS quality and to represent its concepts more formally. Therefore, in this study, it is aimed to develop a solid base for a comprehensive meta-model of OSS quality to create a common understanding among stakeholders. Method: A systematic way has been followed toward developing a common structure, defining a consistent terminology and, finally, providing a meta-model of OSS quality. In this context, (1) the common structure of the quality models for OSS has been investigated, (2) the terms of the general-purpose meta-models of software quality have been analyzed based on the international standards, and (3) the terms of the quality models for OSS have been mapped with the elements of these meta-models. Results: An initial meta-model of OSS quality, which employs a unified structure from the OSS quality models and eliminates the inconsistencies determined in the general-purpose meta-models of software quality, has been proposed and an implementation of this meta-model has been demonstrated. Conclusion: This initial meta-model of OSS quality with a standard terminology can be taken as a guide by researchers who will propose or revise their OSS quality models. It will allow developing multiple OSS quality models with homogenous structure and terms, and also enable comparing the evaluation results obtained by these models.