The intuitionistic fuzzy decision-making problem with high-dimensional data is stu-died in this paper. The general form and operational laws of the intuitionistic fuzzy tensor are defined, the generalized intuitionistic fuzzy weighted averaging (GIFWA) operator based on the intuitionistic fuzzy tensor is subsequently established. By exploring the basic properties of the GIFWA operator, it is proved that the GIFWA operator is a general form of the intuition-istic fuzzy weighted average operator. A novel decision-making method based on the GIFWA operator is presented to solve the intuitionistic fuzzy decision problems with high-dimensional data. One typical example is also provided to demonstrate the efficiency and applicability of our proposed method.