Abstract: The existing methods of curve interpolation cannot solve practical application problems of constructing a closed smooth curve with global convexity for planar convex hull point set. For this purpose, a curve interpolation algorithm for constructing a closed G² continuity curve with global convexity is proposed. A planar convex hull point set was used as interpolating points. The two adjacent convex hull points were used as the first and the fourth control points of a cubic Bézier curve, and the second and the third control points were resolved by the relationship of geometric continuity between the two adjacent Bézier curves. The closed, G² continuity and global convexity properties of the constructed curve were proved theoretically. A simple and effective curve constructing algorithm was presented. The experiment showed that the constructed curve has an explicit physical explanation. The practical application of simulating the measurement path of tape to retrieve stem diameter by the constructed curves verifies the accuracy and practicability of the proposed curve interpolation algorithm.