Summary: We are concerned with the following Choquard equation: \[ - {\varepsilon^2}\Delta u + V(x)u = {\varepsilon^{- \alpha}}({I_\alpha} * F(u)){F^\prime}(u), \quad x \in{\mathbb{R}^N}, \] where \(N \geqslant 4\), \(\alpha \in (0, N)\), \(I_\alpha\) is the Riesz potential and \(\varepsilon > 0\) is a small parameter. Note that \(F(u): = \frac{1}{q} |u|^q + \frac{1}{2_\alpha^*} |u|^{2_\alpha^*}\), where \(2_{\alpha}^{\#} < q < {2_{\alpha}^*}\), and \(2_\alpha^\sharp : = \frac{N + \alpha}{N}\) and \(2_\alpha^* : = \frac{N + \alpha}{N - 2}\) are lower and upper critical exponents in the sense of the Hardy-Littlewood-Sobolev inequality. In this paper, we construct a bound-state concentrating at an isolated component of the positive local minimum points of \(V\) as \(\varepsilon \rightarrow 0\) for each \(q \in (2_{\alpha}^{\#}, 2_{\alpha}^*)\). This result extends some results established in [S. Cingolani and K. Tanaka, Rev. Mat. Iberoam. 35, No. 6, 1885–1924 (2019; Zbl 1431.35169)] for the case \(q < 2\) which was seen as an open problem in [V. Moroz and J. van Schaftingen, Calc. Var. Partial Differ. Equ. 52, No. 1–2, 199–235 (2015; Zbl 1309.35029)]. The proof of the current paper uses variational methods, a truncation technique and a new regularity result that we develop in this work.