The viscosity of the electrolyte in vanadium redox flow batteries (VRFBs) varies during charge and discharge as the concentrations of acid and vanadium ions in the electrolyte continuously change with the state of charge (SOC). In previous VRFB models, however, the electrolyte has been treated as a constant-viscosity solution. In this work, a mass-transport and electrochemical model taking account of the effect of SOC-dependent electrolyte viscosity is developed. The comparison between the present model and the model with the constant-viscosity simplification indicates that the consideration of the SOC-dependent electrolyte viscosity enables (i) a more realistic simulation of the distributions of overpotential and current density in the electrodes, and (ii) more accurate estimations of pumping work and the system efficiency of VRFBs.