  Let $T$ be a $m$-linear Calder\'{o}n-Zygmund operator of type $\omega$ with
$\omega$ being nondecreasing and $\omega \in$ Dini(1) and $[\vec{b},\,T]$ be
the commutator generated by $T$ with symbols $\vec{b}=(b_1,\,\ldots,\,b_m)$
belonging to generalized Campanato spaces. We give necessary and sufficient
conditions for the boundedness of $[\vec{b},\,T]$ on generalized Morrey spaces
with variable growth condition.
