Abstract: Extends the concept and theory of Sugeno integral and fuzzy measure, presents a new method for multi-attribute decision making under interval intuitionistic fuzzy environment. The concept of interval intuitionistic fuzzy-valued fuzzy measure and interval intuitionistic fuzzy-valued Sugeno integral are introduced, and the relationship between the extension and original fuzzy measure and Sugeno integral are represented. Some properties and calculating methods of the extended Sugeno integral are given. A multi-attribute decision making method is established in which interval intuitionistic fuzzy-valued Sugeno integral is taken as its aggregation function. An illustrative example is provided to verify the new method and to demonstrate its feasibility and practicality.