In this paper, we analyze the charge dynamics of ionic polymer-metal composites (IPMCs) in response to voltage inputs composed of a large dc bias and a small superimposed time-varying voltage. The IPMC chemoelectrical behavior is described through the modified Poisson-Nernst-Planck framework, in which steric effects are taken into consideration. The physics of charge build-up and mass transfer in the proximity of the high surface electrodes is modeled by schematizing the IPMC as the stacked sequence of five layers, in which the ionomeric membrane is separated from the metal electrodes by two composite layers. The method of matched asymptotic expansions is used to derive a semianalytical solution for the concentration of mobile counterions and the electric potential in the IPMC, which is, in turn, used to establish an equivalent circuit model for the IPMC electrical response. The circuit model consists of the series connection of a resistor and two complex elements, each constituted by the parallel connection of a capacitor and a Warburg impedance. The resistor is associated with ion transport in the ionomeric membrane and is independent of the dc bias. The capacitors and the Warburg impedance idealize charge build-up and mass transfer in the vicinity of the electrodes and their value is controlled by the dc bias. The proposed approach is validated against experimental results on in-house fabricated IPMCs and the accuracy of the equivalent circuit is assessed through comparison with finite element results.