Summary: In this paper, we develop a new fuzzy multi-criteria group decision making method using triangular intuitionistic fuzzy numbers (TIFNs) for determining critical path in a critical path problem (CPP). The CPP considered here involves both quantitative and qualitative assessments of the decision makers on multiple conflicting criteria. The intuitionistic fuzzy numbers are introduced since they consider both preferences and non-preferences simultaneously and are thus capable of representing qualitatively evaluated information more effectively than fuzzy sets. The proposed method involves fuzzy evaluation based on the extended preference relation of TIFNs using \((\alpha ,\beta )\)-cuts considered for preferences and non-preferences, respectively. The preference intensity function based on the extended preference relation of TIFNs leads to the strength and weakness index scores of the possible paths on given criteria. Furthermore, we define the total performance score of each project path using its strength and weakness index scores. The path that has the highest score is selected as the best alternative in terms of its criticality for the entire project to finish as per the chosen criteria. A numerical illustration is provided to demonstrate working of the proposed methodology.