In this paper, we consider the existence and asymptotic behavior normalized solutions for the following Choquard equation involving Sobolev critical exponent \(-\Delta{u}=\lambda{u}+(I_{\alpha} \ast \ |u|^{q})|u|^{q-2}{u}+|u|^{4}{u}\quad{\rm in} \ {\mathbb R}^{3},\) under the prescribed L2-norm \(\int_{\mathbb R^{3}} \ u^{2}=c^{2}\) with c > 0, where Iα denotes the Riesz potential. Let \({5 \over 3} < q < 3\) . When α > 0 small enough, we obtain the existence of the positive ground state solutions, which converge to a least energy solution of the limiting critical local problem as α → 0+.
