A new mathematical model for facilitated mass transport in a polymeric membrane with a fixed-site carrier was developed by extending the single RC circuit model, which was derived by assuming concentration fluctuation and an analogy between electron transport in a parallel resistor-capacitor (RC) circuit and mass transport in a facilitated transport membrane. Here, a series of parallel RC circuits was employed instead of the single RC circuit to take account of the four diffusion pathways, demonstrating solute transfer betwwen matrix and carrier. It was then examined against the experimental data on oxygen transport through poly(dimethyl siloxane), poly(butyl methacrylate) and poly(methyl methacrylate) with a metallo-porphyrin carrier. The current model showed a better agreement than the single circuit model but the difference was minor.