This paper defines the mixed function with shape parameter α,β, and the curve of the mixed function holds many similar geometrical qualities of Bezier curve. The shape of the curve can be adjusted when changing the value of the shape parameter α,βand this kind of new curve has simple smoothing match condition. This paper gives G2 smoothing match condition between the curves, reveals that the last edge of the first curve’s control polygon and the first edge of the second curve’s control polygon are coincident, and finally uses the examples to illustrate the effectiveness of this modeling method in geometrical shape.