Let Ω be a bounded domain in R^n, n > 2 with 0 ∈ Ω. We consider the Hardy-Sobolev inequality (The equation is abbreviated) for any u ∈ W_0^(1,2) (Ω). In this paper we shall investigate the weighted improvement (1) with finitely many remainder terms involving singular function (The equation is abbreviated) in a ball domain. Here the number of remainder terms depends on the choice of R.