Abstract: The research on the reduction of parametric curves,especially the Bézier curves,has come of age.But the research on the reduction of transcendental curves is rarely reported in literature.This paper studies H-Bézier curves that can exactly represent transcendental curves such as the exponential curves and the catenaries,and gives an approximation method of multidegree reduction of H-Bézier curves by making use of the elevation property of H-Bézier curves,and the theory of generalized inverse matrix.The degree reduction error bound is estimated,the relationship between the reduction of H-Bézier curves and that of Bézier curves is established,and numerical examples are given to show that the presented method has good approximation effects,and hence the theory of H-Bézier curves is enriched.