We fabricate electric double-layer field-effect transistor (EDL-FET) devices on mechanically exfoliated few-layer graphene. We exploit the large capacitance of a polymeric electrolyte to study the transport properties of three, four and five-layer samples under a large induced surface charge density both above and below the glass transition temperature of the polymer. We find that the carrier mobility shows a strong asymmetry between the hole and electron doping regime. We then employ ab initio density functional theory (DFT) calculations to determine the average scattering lifetime from the experimental data. We explain its peculiar dependence on the carrier density in terms of the specific properties of the electrolyte we used in our experiments. (C) 2016 Elsevier B.V. All rights reserved.