With respect to the decision making problems where a lot of fuzzy and grey information always exists in the real-life deci-sion making information system, it is difficult for such uncertainty methods as fuzzy mathematics, probability, and interval numbers to deal with. To this end, based on the thought and method of grey numbers, grey degrees and interval numbers, the concept of dominance grey degree is defined. And then a method of rank-ing interval grey numbers based on the dominance grey degree is proposed. After discussing the relevant properties, the paper final y uses an example to demonstrate the effectiveness and ap-plicability of the model. The result shows that the proposed model can more accurately describe uncertainty decision making prob-lems, and realize the total ordering process for multiple-attribute decision-making problems.