The selection of appropriate machines is one of the most critical decisions in the design and development of an efficient production environment. It is the fact that improper machine selection can result in quality, flexibility, productivity, etc., problems and negatively affect the overall performance and productivity of a manufacturing system. On the other hand, selecting the best machine among many alternatives is a multi-criteria decision making (MCDM) problem. In this paper, a fuzzy-based MCDM approach is used. For this aim, the fuzzy analytic network process (FANP) is used to determine weights of the criteria and preference ranking organization method for enrichment evaluations (PROMETHEE) is used to obtain final ranking of alternative machines. The proposed approach is applied for the selection of a CNC router machine (RM) to be purchased in an international company. In the problem addressed, there are four main criteria, namely cost, quality, flexibility and performance with the corresponding fourteen sub-criteria. The results for the case study indicate the best machine among six potential alternatives and provide different managerial insights for the decision makers.