Abstract: In order to overcome the drawbacks of the existing methods, a convexity-preserving interpolation method based on the intrinsic properties of a set of convex data points is proposed. The method introduces the concept of the generalized convexity of data points. For a set of generalized convex data points, directly insert the control points of Bézier segment into every two data points according to the direction of the polyline produced by the data points; The control points are obtained by the condition of its convexity being the same as that of the data points, and by assuming the smooth connecting between two adjacent Bézier segments; The control points of every Bézier segment are only determined by 4 adjacent data points, thus the curve is local shape adjustable. Some examples show that the method is very efficient, and the theory derivation is also right.