Project management is of great importance in today's business world in the wake of the fourth industrial revolution, which is bringing significant changes to everyday business and all areas of life, including project management and project quality. The role of quality is extremely important in these circumstances, because improving the quality of products and the organization makes production more efficient, increases customer satisfaction, and maintains and improves the company's competitive position in the market. The aim of this master thesis is to highlight the importance and role of quality in project management in the context of Industry 4.0 and to show, using the example of a real organization (the company "Đuro Đaković Termoenergetska postrojenja d.o.o."), how traditional quality concepts can be adapted to the new trends and technologies of Industry 4.0, with the aim of achieving excellence in business and maintaining competitiveness on the market in the field of project-type production. In this master thesis, the methods of quality monitoring in the project of manufacturing pressure equipment for a boiler plant in the company "Đuro Đaković Termoenergetska postrojenja d.o.o." are presented, focusing on the problem of remote visual inspection. Quality management is analyzed by examining the legal and technical regulations and following the process of quality control on a particular project from the manufacture of the pressure equipment to the final measurements. The process of product quality control is carried out in this company with the help of information and communication technologies, using the NCR application (Nonconformity report application) and modern measuring devices that provide results in real time, so that all projects meet the quality defined according to the company's policy, but also according to the requirements of the customers. The company is continuously developing business models that meet the challenges of the present and the future, but there is still room for improvement in the quality management of the projects. In this thesis, a proposal is presented to implement the traditional method of Total Quality Management (TQM) in combination with a modern tool - NCR software and HRN standards ISO 10006:2018 - Quality Management - Guidelines for Quality Management in Projects (ISO 10006:2017) - with the aim of gradually achieving a digitized TQM, i.e. Quality 4.0 using Industry 4.0 technologies, so that the company can continue to be successful and competitive in today's turbulent market conditions.