Abstract: This paper investigates degree elevation of interval B-spline.Based on the concept of interval control polygon, we prove that interval B-spline curves hold the degree elevation property by using bi-degree B-spline basis functions.Further, we show that the degree elevation of interval B-spline curves is equivalent to corner cutting of control polygons.Finally, it's proved that the control polygon sequence by degree elevation will converge to the interval B-spline curve.