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This paper studies the α-consensus value of a cooperative game with payoffs of triangular intuitionistic fuzzy numbers and gives the formation mechanism of the α-consensus value, as well as some properties. Using the extended Hukuhara difference of triangular intuitionistic fuzzy numbers, the α-consensus value of the triangular intuitionistic fuzzy cooperative game is obtained. Furthermore, we study the condition of the α-consensus value satisfying the individual rationality, which makes the α-consensus value of the cooperative game more practical in real problems. Finally, a numerical example is given to illustrate the validity and applicability of the α-consensus value of the triangular intuitionistic fuzzy cooperative game proposed in this paper.