Abstract: This paper proposes a new method for curve metamorphosis，where the in-between curves are constructed by using unstructed meshes.The key idea is to implicitly represent the curve as the level set of a higher dimensional function，and solve the morphing equations on unstructed meshes using finite volume methods.This approach thereby eliminates the round-off errors taken by the interpolation in a Cartesian coordinate system.Experimental result is presented to demonstrate the effectiveness of this method.