Abstract：The properties of strong consistent interval judgment matrix in literatures are not well studied both at home and abroad, so the priority method research lacks a theoretical basis. The properties and priority problems of strong consistent interval judgment matrix are studied in this paper. First, some concepts including the interval judgment matrix, the strong consistent interval judgment matrix and the normalized interval vector are explained. Then, a linear programming model is used to derive the normalized interval weights from the strong consistent judgment matrix. On that basis, an equivalent condition of strong consistency for interval judgment matrix is put forward. A nonlinear programming model is developed to generate interval weights for the interval comparison matrix with satisfactory consistency. Finally, two numerical examples are provided to illustrate the validity of the proposed method, and it is shown that the nonlinear programming model can also be applyied to consistent interval judgment matrix and satisfactory consistent interval judgment matrix. The properties and the ranking method may further improve the consistency theories of interval judgment matrix.