  Let $\Gamma$ be a torsionless commutative cancellative monoid and $R
=\bigoplus_{\alpha \in \Gamma}R_{\alpha}$ be a $\Gamma$-graded integral domain.
In this paper, we introduce the notion of graded going-down domains. Among
other things, we provide an equivalent condition for graded-Pr\"{u}fer domains
in terms of graded going-down and graded finite-conductor domains. We also
characterize graded going-down domains by means of graded divided domains. As
an application, we show that the graded going-down property is stable under
factor domains.
