The aim of this paper is to develop a methodology for solving matrix games with payoffs of trapezoidal intuitionistic fuzzy numbers (TrIFNs). In this methodology, the concepts of TrIFNs and solutions for matrix games with payoffs of TrIFNs are defined. Two new auxiliary intuitionistic fuzzy nonlinear programming models are hereby constructed to solve matrix games with payoffs of TrIFNs. Using a new ranking method based on the value and ambiguity of TrIFNs, the auxiliary intuitionistic fuzzy nonlinear programming models are transformed into the bi-objective parameterized nonlinear programming models, which are further integrated into the parameterized linear programming models, which are used to obtain solutions of matrix games with payoffs of TrIFNs. The validity and applicability of the proposed methodology in this paper are illustrated with a numerical example.