We consider a quasilinear Choquard problem \(\begin{aligned} \left\{ \begin{aligned}&-\text {div}(\beta (|\nabla u|^2)\nabla u)+(\lambda +V(x))u=(I_\theta *|u|^p)|u|^{p-2}u\ &\text {in}\ \mathbb {R}^{N\ge 3},\\&u(x)\rightarrow 0,\ &|x|\rightarrow +\infty \end{aligned} \right. \end{aligned}\) with the prescribed mass \(\int _{\mathbb {R}^N}|u|^2\text {d}x=a^2\) for a fixed \(a>0\) , where \(\lambda \in \mathbb {R}\) is a Lagrange multiplier and \(I_\theta \) is the Riesz potential of \(\theta \) -th order with \(\theta \in (0,N)\) . We first prove the existence of normalized ground state solutions to this problem with the mass subcritical case and \(V(x)\equiv 0\) by imposing some suitable conditions on \(\beta (\cdot )\) . We next attain the existence of radially normalized ground state solutions to this problem with the mass supercritical case and \(V(x)\le 0\) by means of mountain pass theorem. Finally, we show the nonexistence of its normalized solutions with the mass critical case.
