Safety in the sustainable construction is a game with uncertain reality, with human’s life. Managers in power, involved in the construction project life cycle, create rules for the game and are the main players. The project’s success can be perceived differently by stakeholders. A company’s competitiveness, successful implementation of the projects and effective safety management depends on the strategic allocation of its human resources in order to select a proper project team in alignment with employee capabilities. This requires detailed factors reflecting their role (in line with their interests and attitudes) and knowing which of them has a decisive influence on the successful implementation of the project. The real data describing key factors in this concept can be provided as uncertain conditions. This work presents a novel integrated modified fuzzy group decision-making approach to select and rank the most influential persons ensuring the sustainable prevention of accidents at work in the small and medium-sized construction enterprises. This model includes the Delphi method and fuzzy extensions of Eckenrode’s criteria rating method. The proposed model could be expanded in order to select the most suitable individuals for sustainable management of safety and, moreover, for the effective implementation of safety and health measures.