Abstract: Based on the gray system theory，the multi-attribute decision making problem is discussed，in which both the attribute values and the attribute weights are interval gray numbers.By introducing the integrated incidence degree method together with some relational concepts based on ideal and critical projects，a linear programming model which also considers the attribute weights is presented，which extends the classical gray incidence decision-making to the case of interval gray numbers.Finally，an example shows the rationality of gray incidence decision-making and the validity of the arithmetic mentioned above.