We propose to investigate the solutions of system of functional-integral equations in the setting of measure of noncompactness on real-valued bounded and continuous Banach space. To achieve this, we first establish some new Darbo type fixed and coupled fixed point results for µ-set (ω, ϑ)-contraction operator using arbitrary measure of noncompactness in Banach spaces. An example is given in support for the solutions of a pair of system of functional-integral equations. © 2021, Semnan University, Center of Excellence in Nonlinear Analysis and Applications. All rights reserved.