With regard to intuitionistic fuzzy multiple attribute decision making with interaction between attributes, a method based on the Zhenyuan integral is presented. The intuitionistic fuzzy Zhenyuan averaging(IFZA) operator is developed, and some of its desirable properties are studied. The research shows that the IFZA operator can fully consider the importance of interactions among different attributes and improve the intuitionistic fuzzy Choquet integral operator. Finally, a method based on the IFZA for intuitionistic fuzzy multiple attribute decision making is introduced, and a numerical example is provided to illustrate the effectiveness and applicability of the presented method.