In this paper, we study the existence of normalized multi-bump solutions for the following Choquard equation: \(\begin{aligned} -\epsilon ^2\Delta u +\lambda u=\epsilon ^{-(N-\mu )}\left( \int _{\mathbb {R}^N}\frac{Q(y)|u(y)|^p}{|x-y|^{\mu }}{\textrm{d}}y\right) Q(x)|u|^{p-2}u, \text {in}\ \mathbb {R}^N, \end{aligned}\) where \(N\ge 3\) , \(\mu \in (0,N)\) , \(p\in \left( \frac{2N-\mu }{N}, \frac{2N-\mu }{N-2}\right) \setminus \left\{ \frac{2N-\mu +2}{N}\right\} \) , \(\epsilon >0\) is a small parameter and \(\lambda \in \mathbb {R}\) appears as a Lagrange multiplier. By developing a new variational approach, we show that this problem has a family of normalized multi-bump solutions focused on the isolated part of the local maximum of the potential Q(x) for sufficiently small \(\epsilon >0\) . The asymptotic behavior of the solutions as \(\epsilon \rightarrow 0\) is also explored. It is worth noting that our results encompass the sublinear case \(p<2\) , which complements some of the previous works.