  Let $(X,d,\mu)$ be a metric measure space satisfying both the geometrically
doubling and the upper doubling measure conditions, which is called
non-homogeneous metric measure space. In this paper, via a sharp maximal
operator, the boundedness of commutators generated by multilinear singular
integral with $RBMO(\mu)$ function on non-homogeneous metric measure spaces in
$m$-multiple Lebesgue spaces is obtained.
