  We consider a finite acyclic quiver $\mathcal{Q}$ and a quasi-Frobenius ring
$R$. We endow the category of quiver representations over $R$ with a model
structure, whose homotopy category is equivalent to the stable category of
Gorenstein-projective modules over the path algebra $R\mathcal{Q}$.
  As an application, we then characterize Gorenstein-projective
$R\mathcal{Q}$-modules in terms of the corresponding quiver
$R$-representations; this generalizes a result obtained by Luo-Zhang to the
case of not necessarily finitely generated $R\mathcal{Q}$-modules, and
partially recover results due to Enochs-Estrada-Garc\'ia Rozas, and to
Eshraghi-Hafezi-Salarian. Our approach to the problem is completely different
since the proofs mainly rely on model category theory.
