In this paper, we study the following biharmonic Hartree problem \(\begin{aligned} \left\{ \begin{array}{ll} \Delta ^2 u=\left( \int _{\Omega }\frac{ u^{2^{*}_{\alpha }}(y)}{|x-y|^{\alpha }}\textrm{d}y\right) u^{2^{*}_{\alpha }-1}+\varepsilon u~ & \quad \textrm{in}~~ \Omega ,\\ u=\Delta u=0 ~ & \quad \textrm{on} ~~ \partial \Omega , \end{array} \right. \end{aligned}\) where \(N\ge 8\) , \(\alpha \in (0,8)\) , \(2^{*}_{\alpha }=\frac{2N-\alpha }{N-4}\) is the upper critical exponent with respect to the Hardy-Littlewood-Sobolev inequality, \(\Omega \) is a bounded smooth domain in \(\mathbb {R}^{N}\) and \(\varepsilon >0\) is a small parameter. By applying the reduction arguments, we prove that the above problem has a family of solutions \(u_{\varepsilon }\) concentrating around the critical point of Robin function as \(\varepsilon \rightarrow 0\) .
