In a manufacturing system, inappropriate machine selection may lead to many problems by negatively affecting productivity, precision, flexibility and product quality, and machine selection is considered to be an important subject to make the system effective. A Multi-Criteria Decision Making (MCDM) which is relying on the different criteria and alternatives is to choose the most suitable machine among many alternatives. In this study, for machine selection problem, a hybrid approach is proposed which combines Analytic Network Process (ANP) and Grey Relational Analysis (GRA). To identify weights of the selection criteria and to analyze the machine selection problem, the ANP is used whilst the GRA is used for ranking. The proposed approach can be applied easily by anybody (technical staff, managers, manufacturer, vendor, etc.) familiar with basic Microsoft Excel knowledge. The proposed approach is used for the selection problem of CNC router machines to be bought by an international company. As a result, the company has considered the method and outcomes acceptable and appropriate to implement to the machine selection decisions.