Abstract: In computer aided geometric design,an interpolation curve restricted on a given smooth surface is a new research aspect.The main solution is to transfer to the common curve interpolation based on the relation between the surface and its parameter domain.A new and practical method is introduced in this paper.The basic idea is as follows:at first the given data points and tangent vectors on the surface are projected to a plane,then construct a spline curve interpolating the projected data points on the plane.The intersect curve of the surface and the projecting cylinder of the spline curve is the G1 continous interpolation curve.

Key words: BÉ, zier curve；interpolating curve；spline curve；G¹ continuity