Abstract: The minimum distance computation problem has wide applications in CAD/CAM and computer graphics.This paper presents a sweeping sphere pruning based method for computing the minimum distance between a Bézier curve and a Bézier surface.Firstly,we provide a sufficient condition whether a curve is outside of the sweeping sphere of a surface,or whether a surface is outside of the sweeping sphere of a curve,which can prune most of sub-curves or surface patches which contain no closest point.Then we provide conditions whether the closest point is an end point of the curve or on a boundary curve of the surface,this turns the curve/surface case into a curve/curve or point/surface case,and leads to lower computation complexity and better efficiency.Examples illustrate the efficiency and the robustness of the new method.