Zinc oxide varistors are among the most important surge arresters. The current-voltage (I–V) behaviour of these devices can be approximated by a model of electrical networks of grain boundaries arranged in 3D space, where nonlinear resistors mimic the effective grain boundary behaviour of the varistor microstructure. A simplified version of the network model, namely parallel circuits of chains of serially connected resistors of different length (path model), is derived from a fully 3D model of the polycrystalline microstructure. A comparison of the path model with a complex resistor network based on the 3D model demonstrates that the network of highly nonlinear resistors has a very similar DC I–V characteristic as parallel paths of these resistors connected in series. The path model, whose parameters were adapted from microscopic I–V measurements, is able to reproduce the macroscopic I–V behaviour of real low-voltage zinc oxide varistors.