Abstract: Combining the concepts of fuzzy set theory, entropy, ideal, and grey relation analysis, a fuzzy grey relation method for multiple criteria decision-making problems is proposed. First, triangular fuzzy numbers and linguistic values characterized by triangular fuzzy numbers are used to evaluate the importance weights of all criteria and the superiority of all alternatives versus various criteria above the alternative level. Then, the concept of entropy is utilized to solve the adjusted integration weight of all objective criteria above the alternative level. Furthermore, using the concepts of ideal, the grey ration grades of various alternatives versus ideal solution are ranked to determine the best alternative. Finally, a numerical example of selecting most appropriate company to build a new highway is used to demonstrate the applicability of proposed method. The study results show that this method is an effective means for tackling MCDM problems in fuzzy and grey environments.