Project management frameworks describe the preferred approaches to project quality management, as well as applicable methods and tools. Despite this, quality problems in the construction project are still widespread. This study aimed to identify crucial quality-related factors in construction project management and find relations between them, to help researchers and project managers better respond to quality issues. A systematic literature review (SLR) was used to identify previous studies on quality-related factors. Literature review and further quantitative analysis revealed that quality-related factors are related to three categories: Quality of project process, quality of organisational processes, and quality of results (products), which together create the quality of the whole construction project. The results highlight quality-related factors (14 related to the quality of processes, 6 to quality of an organisation, and 13 to quality of products) that should be taken into account in further research, as well as planning and executing construction projects. Their inclusion at the planning stage should help project managers, sponsors, and steering committees avoid or minimise quality-related problems. Moreover, this study sheds an interesting light on quality. We found that the quality of processes and quality of an organisation has precedence over the final product quality. Based on the results of the study, structural equation modelling (SEM) was used to create a null model that will be the starting point for further research in the construction enterprises.