Summary: We consider asymptotic behaviors of star-shaped curves expanding by \(V=1-K\), where \(V\) denotes the outward-normal velocity and \(K\) curvature. In this paper, we show the followings. The difference of the radial functions between an expanding curve and circle has its asymptotic shape as \(t\to +\infty \). For two curves, if the asymptotic shapes are identical, then the curves are also. The set of all asymptotic shapes is dense in \(C(S^1)\).