Quadratic trigonometric polynomial Bézier curves with a shape parameter are presented in this paper. The trigonometric polynomial curves retain the main superiority of the quadratic Bézier curves. With the shape parameters, the trigonometric polynomial curves can approach more to the quadratic Bézier curves or to the given control polygon than the quadratic Bézier curves. Shape parameters have the property of geometry, the larger is the parameter,the more the curves approach to the control polygon. The curves represent ellipse and circle precisely. The G2 and C3continuity condition of twopiece trigonometric polynomial Bézier curves are also discussed.