  In this paper, we study the following quasilinear Schr\"{o}dinger equation of
Choquard type $$ -\triangle u+V(x)u-\triangle (u^{2})u=(I_\alpha
*|u|^p)|u|^{p-2}u, \ \ x \in \mathbb{R}^{N}, $$ where $N\geq 3$,\ $0<\alpha<N$,
$\frac{2(N+\alpha)}{N}\leq p<\frac{2(N+\alpha)}{N-2}$ and $I_\alpha$ is a Riesz
potential. Under appropriate assumptions on $V(x)$, we establish the existence
of positive solutions.
