As a novel family member of the redox flow batteries (RFBs), the single flow zincnickel battery (ZNB) without ion exchange membranes has attracted a lot of interests in recent years due to the high charging and discharging efficiencies. To understand the electrical behaviour is a key for proper battery management system. Unlike the electrochemical mechanism models and equivalent circuit models, the neural network based black-box model does not need knowledge about the electrochemical reactions and is a promising and adaptive approach for the ZNB battery modelling. In this paper, a compact radial basis function neural network is developed using a two-stage layer selection strategy to determine the network structure. While Jaya optimization is utilized to determine the non-linear parameters in the selected hidden nodes of the resultant RBF neural network (RBF-NN) model. The proposed method is implemented to model the ZNB to capture the non-linear electric behaviours through the readily measurable input signals. Experimental results manifest the accurate prediction capability of the resultant neural model and confirm the effectiveness of the proposed approach.