The authors researches on the problem of the multiple criteria decision making under risk that attribute weight is completely unknown and criteria values are interval grey numbers. The method of grey multiple criteria decision making under risk based on priority index is proposed. By using the possibility, the priority index matrix and analytical technique of comparing interval grey numbers, the former problem is converted to no risky multiple criteria problems, in which criteria values are real numbers. By using information entropy to determine the attribute weight, the authors states two corresponding algorithms to attain the ranking of alternatives and choosing the best. In the final, one example is given to illustrate the validity and efficiency of two algorithms.