The　aim　of　this　paper　is　to　develop　a　new　methodology　for　solving　bi-matrix　games　with　payoffs　of　Atanassov’s　intuitionistic　fuzzy　(I-fuzzy)　numbers.　In　this　methodology,　we　define　the　concepts　of　I-fuzzy　numbers,　the　value-index　and　ambiguity-index,　and　develop　a　difference-index　based　ranking　method.　Hereby　the　parameterized　non-linear　programming　models　are　derived　from　a　pair　of　auxiliary　I-fuzzy　mathematical　programming　models,　which　are　used　to　determine　solutions　of　bi-matrix　games　with　payoffs　represented　by　I-fuzzy　numbers.　Validity　and　applicability　of　the　models　and　method　proposed　in　this　paper　are　illustrated　with　a　practical　example.　©　2015,　Taiwan　Fuzzy　Systems　Association　and　Springer-Verlag　Berlin　Heidelberg.