This paper is concerned with the following elliptic equation with Hardy potential and critical Sobolev exponent \begin{align*} \Delta(|\Delta u|^{p-2}\Delta u)-ambda \frac{|u|^{p-2}u}{|x|^{2p}}=\mu h(x)|u|^{q-2}u+|u|^{p^{*}-2}u\quad ext{in }mega , \quad uı W^{2,p}_0(mega). \end{align*} By means of the variational approach, we prove that the above problem admits a nontrivial solution.