A method for constructing shape-reserving planar C¹ quadratic Bézier interpolation spline by minimizing the stretch energy is proposed in this paper. Because the C¹ quadratic Bézier interpolation spline can be determined only by the second control point of the first interpolation curve, we give the method for determining the second control point of the first interpolation curve by minimizing the stretch energy. We prove that the C¹ quadratic Bézier interpolation spline constructed by the proposed method is shape preserving. Some numerical examples show that the proposed method has good effect.