The soluble lead-acid battery is a redox flow cell that uses a single reservoir to store the electrolyte and does not require a microporous separator or membrane, allowing a simpler design and a substantial reduction in cost. In this paper, a transient model for a reversible, lead-acid flow battery incorporating mass and charge transport and surface electrode reactions is developed. The charge-discharge behavior is complicated by the formation and subsequent oxidation of a complex oxide layer on the positive electrode surface, which is accounted for in the model. The full charge/discharge behavior over two cycles is simulated for many cases. Experiments measuring the cell voltage during repeated charge-discharge cycles are described, and the simulation results are compared to the laboratory data, demonstrating good agreement. The model is then employed to investigate the effects of variations in the current density on the performance of the battery.