To solve decision-making problems having the characteristics of grey systems, the three-parameter interval grey number is introduced to measure the evaluation index. The evaluation matrix is standardized from two aspects: type consistency and nondimensionalization. Taking into account the upper and lower limits as well as the center point of the three-parameter interval grey number, the sorting method and distance calculation method of the three-parameter interval grey number based on possibility are put forward. A technique for order preference by similarity to ideal solution (TOPSIS) decision-making method based on three-parameter interval grey numbers is proposed. Finally, an example is given to demonstrate the validity and effectiveness of the method.