Summary: Boundedness of multilinear Littlewood-Paley operators on variable exponent function spaces are studied. Based on the boundedness of the general Littlewood-Paley operator \({g_\varphi}\) on a Lebesgue space, using the boundedness of the sharp maximal operator on variable Lebesgue space \({L^{p(\cdot)}}\), the boundedness of a multilinear Littlewood-Paley operator on a variable exponent Lebesgue space and a variable exponent Herz-Morrey space are obtained.