The concept of intuitionistic N-fuzzy set (INFS) has been applied to the quasi ideals of bi-ternary semigroups. The notion of intuitionistic N-fuzzy quasi ideal of bi-ternary semigroup has been introduced and characterized by using intuitionistic N-fuzzy level set and N characteristic function. The relationships between intuitionistic N-fuzzy quasi ideal and intuitionistic N-fuzzy ideals (left, right, bi) have been discussed. Finally, the idea of translations on intuitionistic N-fuzzy bi-ternary semigroup is discussed.