Summary: In this paper, we investigate the non-autonomous Choquard equation \[ -\Delta u+\lambda V(x)u=(I_{\alpha}\ast F(u))F^{\prime}(u)\quad\text{in } \mathbb{R}^N, \] where \(N\geq 4, \lambda>0, V\in C(\mathbb{R}^N,\mathbb{R})\) is bounded from below and has a potential well, \(I_{\alpha}\) is the Riesz potential of order \(\alpha\in (0,N)\) and \(F(u)=\frac{1}{2_{\alpha}^*}\vert u\vert^{2_{\alpha}^*}+\frac{1}{2_*^{\alpha}}\vert u\vert^{2_*^{\alpha}}\), in which \(2_{\alpha}^* =\frac{N+\alpha}{N-2}\) and \(2_*^{\alpha}=\frac{N+\alpha}{N}\) are upper and lower critical exponents due to the Hardy-Littlewood-Sobolev inequality, respectively. Based on the variational methods, by combining the mountain pass theorem and Nehari manifold, we obtain the existence and concentration of positive ground state solutions for \(\lambda\) large enough if \(V\) is nonnegative in \(\mathbb{R}^N\); further, by the linking theorem, we prove the existence of nontrivial solutions for \(\lambda\) large enough if \(V\) changes sign in \(\mathbb{R}^N\).