In this paper, we consider the following critical Hardy-Sobolev-Maz’ya problem
\begin{cases}-\Delta u=\frac{|u|^{2^*(t)-2} u}{|y|^t}+\mu|u|^{q-2} u & \text { in } \Omega, \\ u=0 & \text { on } \partial \Omega,\end{cases}
where Ω is an open bounded domain in ℝN , which contains some points (0,z*), \mu>0,1<q<2,2^*(t)=\frac{2(N-t)}{N-2}, 0 ≤ t < 2, x = (y, z) ∈ ℝk × ℝN−k, 2 ≤ k ≤ N. We prove that if $N > 2{{q + 1} \over {q - 1}} + t$, then the above problem has two disjoint and infinite sets of solutions. Here, we give a positive answer to one open problem proposed by Ambrosetti, Brezis and Cerami in [1] for the case of the critical Hardy-Sobolev-Maz’ya problem.