Buildings, but especially commercial buildings, are mainly responsible for the energy consumption and greenhouse gas emission. Although energy consumption profiles may vary, heating, ventilating and air conditioning (HVAC) systems and lighting are the major energy users in buildings. HVAC systems constitute several parts and the air handling unit (AHU) is one of the most important components as it uses a significant amount of the energy and its initial cost is relatively higher than the other parts. Therefore, selecting the most appropriate HVAC-AHU system and its supplier plays a significant role in improving the energy efficiency of air-conditioned buildings and thereby obtaining a good score from the green certification system according to which the project in question is evaluated. In general, multiple decision makers, who may have different viewpoints and prefer to express their evaluations by linguistic terms, are in charge of selecting the proper HVAC-AHU system and its supplier from several possible alternatives considering numerous compromising and conflicting criteria simultaneously. This paper employs fuzzy Evaluation Based on Distance from Average Solution (Fuzzy EDAS) method for solving the HVAC-AHU system and its supplier selection problem for a green multifunctional shopping centre project located in Moscow. After obtaining the results and determining the optimal solution, sensitivity analysis was carried out to show the stability of the results. The decision makers found the method applicable and practical.