Let ( $${\cal X}$$ , d,μ) be a non-homogeneous metric measure space satisfying the so-called upper doubling and geometrically doubling conditions, which includes the space of homogeneous type and the Euclidean space with the non-doubling measure as special cases. Let T be a multilinear Calderon-Zygmund operator and $$\vec b: = ({b_1}, \ldots ,{b_m})$$ be a finite family of $$\widetilde{{\rm{RBMO}}}(\mu)$$ functions. In this paper, some weak-type multiple weighted estimates for the iterated commutator $${{\rm{T}}_{\Pi \vec b}}$$ generated by T and $$\vec b$$ are obtained.