The aim of this paper is to study the existence of stable standing waves for the following nonlinear Schr\”{o}dinger type equation with mixed power-type and Choquard-type nonlinearities \[ i\partial_t \psi+\Delta \psi+\lambda | \psi|^q \psi+\frac{1}{|x|^\alpha}\left(\int_{\mathbb{R}^N}\frac{| \psi|^p}{|x-y|^\mu|y|^\alpha}dy\right)| \psi|^{p-2} \psi=0, \] where $N\geq3$, $0<\mu0$, $\alpha\geq0$, $2\alpha+\mu\leq{N}$, $0