Summary: In the shape blending process, the parametric continuity of the blending curves is not always preserved. In this paper, firstly, an HC Bézier-like curve is defined, the parametric continuity preserving problems of blending curves are investigated by using the boundary properties of the HC Bézier-like curve. Especially, in the linear blending process, the maintenance conditions of the first order and the second order parametric continuities are derived, and several solutions are discussed. The algorithms can be used in robot working, highway design and industry design which often use C-shape and S-shape.