A minimum ring-band mathematical definition :In the done ring-band, there are at least two inner points and two outer points which scatter staggeringly on the circumference. With this definition as the rule of searching calculation' s ending,a fast numerical algorithm of gaining the minimum ring-band of a closed curve was suggested:Make a ring-band with the four points scattered staggeringly,then replace the old points with new ones continuously until all the points are located within the ring-band. The method was used in an application example to measure the spindle rotating precision of machine tools.