Abstract: This paper presents a G¹ circular arc interpolation algorithm.We first choose part of the data points satisfying some conditions to construct the initial circles.Then with the left data points we construct circles which are tangent to the neighbor initial circles.In the process,all the data points should be the inner points of corresponding circular arc. Moreover,the best effort is made to ensure that there are two data points on each circular arc.The resulting curve keeps the start tangent and end tangent,and the segment number of circular arcs is less than that of data points.Additionally,the interpolating curves can preserve the shape of original data well.