Due to the increasing trend of using renewable energy, the development of an energy storage system (ESS) attracts great research interest. A zinc–air battery (ZAB) is a promising ESS due to its high capacity, low cost and high potential to support circular economy principles. However, despite ZABs' technological advancements, a generic dynamic model for a ZAB, which is a key component for effective battery management and monitoring, is still lacking. ZABs show nonlinear behaviour where the steady-state gain is strongly dependent on operating conditions. The present study aims to develop a dynamic model, being capable of predicting the nonlinear dynamic behaviour of a refuellable ZAB, using a linear parameter-varying (LPV) technique. The LPV model is constructed from a family of linear time-invariant models, where the discharge current level is used as a scheduling parameter. The developed LPV model is benchmarked against linear and nonlinear model counterparts. Herein, the LPV model performs remarkably well in capturing the nonlinear behaviour of a ZAB. It significantly outperforms the linear model. Overall, the LPV approach provides a systematic way to construct a robust dynamic model which well represents the nonlinear behaviour of a ZAB.