Let $(A, m)$ be a Noetherian local ring of dimension d. Denote by $e_i(q)$ the i-th Hilbert coefficient of ideal q and $\Lambda_i(A) = {e_i(q) | q is parameter ideals of }.$ Recently, Goto and Ozeki[Contemporary Math.]  proved that  $\Lambda_i(A)$  is finite for all $i = 1,..d$ if and only if A is a generalized Cohen-Macaulay ring. In this talk, we will give another way of the proof shorter than the  proof of Goto and Ozeki.