The vanadium redox flow battery (VRFB) is an attractive grid scale energy storage option, but high operating cost prevents widespread commercialization. One way of mitigating cost is to optimize system performance, which requires an accurate model capable of predicting cell voltage under different operating conditions such as current, temperature, flow rate, and state of charge. This paper presents a lumped isothermal VRFB model based on principles of mass transfer and electrochemical kinetics that can predict transient performance with respect to the aforementioned operating conditions. The model captures two important physical phenomena: (1) mass transfer at the electrode surface and (2) vanadium crossover through the membrane. Mass transfer effects increase the overpotential and thus reduce the battery output voltage during discharge. Vanadium crossover causes a concentration imbalance between the two half-cells that negatively affects the voltage response particularly after long term cycling. Further analysis on the system linearity is conducted to assess the feasibility of using a linear control design methodology.