AbstractThe main purpose of this paper is to prove that the boundedness of the commutator$\mathcal{M}_{\kappa,b}^{*} $generated by the Littlewood-Paley operator$\mathcal{M}_{\kappa}^{*} $and RBMO (μ) function on non-homogeneous metric measure spaces satisfying the upper doubling and the geometrically doubling conditions. Under the assumption that the kernel of$\mathcal{M}_{\kappa}^{*} $satisfies a certain Hörmander-type condition, the authors prove that$\mathcal{M}_{\kappa,b}^{*} $is bounded on Lebesgue spacesLp(μ) for 1 <p< ∞, bounded from the spaceLlogL(μ) to the weak Lebesgue spaceL1,∞(μ), and is bounded from the atomic Hardy spacesH1(μ) to the weak Lebesgue spacesL1,∞(μ).