Abstract The rational quadratic trigonometric Bézier curve with two shape parameters is presented in this paper, which is new in literature. The purposed curve inherits all the geometric properties of the traditional rational quadratic Bézier curve. The presence of shape parameters provides a control on the shape of the curve more than that of traditional Bézier curve. Moreover the weight offers an additional control on the curve. Simple constraints for shape parameters are derived using the end points curvature so that their values always fall within the defined range. The composition of two segments of curve using G2 and C2 continuity is given. The new curves can accurately represent some conics and best approximates the traditional rational quadratic Bézier curve.