Project selection is considered as an important problem in project management. It is multi-criteria in nature and is based on various quantitative and qualitative factors. The main purpose of this paper is to present a new rank-based method for project selection in outranking relation. According to this approach, decision alternatives were clustered in the concordance matrix and the discordance matrix through the Electre model based on intuitionistic trapezoidal fuzzy numbers. Then, the two matrices were integrated and ranked using grey relational coefficients and the Minkowski space distance. The results of the model were compared with grey relational projection method with intuitionistic trapezoidal fuzzy number. To illustrate the proposed methodology, a case study was conducted to select National Iranian Oil Company projects.