This paper presents a fractional-order model (FOM) for lithium-ion batteries and its parameter identification using time-domain test data. The FOM is derived from a modified Randles model and takes the form of an equivalent circuit model with free non-integer differentiation orders. The coefficients and differentiation orders of the FOM are identified by hybrid multi-swarm particle swarm optimization. The influence of approximation degree on model accuracy is discussed. Battery datasets under a range of conditions are used to analyze model performance. The accuracy and robustness of the FOM are benchmarked against the commonly used first-order RC equivalent circuit model. (C) 2015 Elsevier B.V. All rights reserved.