The hysteresis of the open-circuit voltage as a function of the state-of-charge in a 20Ah lithium-iron-phosphate battery is investigated starting from pulsed-current experiments at a fixed temperature and ageing state, in order to derive a model that may reproduce well the battery behaviour. The hysteretic behaviour is modelled with the classical Preisach model used in magnetic materials. The paper shows that the Preisach model can successfully be applied to the lithium-ion battery hysteresis. First, the model is discretised by using the Everett function and identified by means of experiments, in which first-order reversal branches are measured. Then, the model is simulated and compared to some experimental data collected with different current profiles and to a one-state variable model previously used in the literature. The results show that the hysteresis is well reproduced with rms errors around 2%. The advantages of the Preisach-based method, when compared to other models, are the formal and repeatable identification procedure and the limited computational resources needed for the model simulation that makes it appropriate for the online implementation on low-complexity hardware platforms.