Electrical transport in zinc oxide varistors is simulated using two‐dimensional Voronoi networks. The networks are assumed to contain randomly distributed grain boundaries of three electrical types: (1) high nonlinearity (i.e., ‘‘good’’) junctions; (2) poor nonlinearity (i.e., ‘‘bad’’) junctions; and (3) linear with low‐resistivity (i.e., ohmic) junctions. These type classifications are those found in experimental measurements. By varying the type concentrations, the simulated current density versus electric field (J–E) characteristics can be made to conform to the different experimentally observed characteristics of ZnO varistors. These characteristics include the sharpness of switching at the transition between ohmic and nonlinearJ–Eresponse (i.e., knee region), as well as the degree of nonlinearity. It is shown that the reduction of the nonlinearity coefficient of bulk varistors, relative to that of isolated grain boundaries, can be explained only by the presence of ‘‘bad’’ varistor junctions. ©1996 American Institute of Physics.