The sequence of interval grey numbers is a kind of basic research objects of grey prediction. Based on grey degree information contained in the interval grey numbers, a grey model of interval grey numbers based on the axiom of generalized non-decrease grey degree is established by fully excavating and expanding the connotation of non-decrease grey degree axiom. To be specific, the upper and lower bounds of interval grey numbers are unifiedly processed by using the quasi grey factor to maximize each interval grey number’s grey degree, which can ensure the fulfillment of the axiom of “non-decrease grey degree”in the subsequent modeling process. Then, according to the trend of grey degree sequence of interval grey numbers, the grey prediction model of grey degree sequence is predicted to obtain grey factor which can correct the reliability of the previous model deeply. Finally, the effectiveness and practicability of the proposed model are verified by empirical results.