A numerical model is developed to predict transient behaviors of electric vehicle lead-acid batteries during discharge and charge processes. The model not only accounts for coupled processes of electrochemical kinetics and mass transport occurring in a battery cell, but also considers free convection resulting from density variations due to acid stratification. A single set of conservation equations valid for both porous electrodes and the free electrolyte region is derived and numerically solved using a computational fluid dynamics technique. This numerical methodology is capable of simulating a two-dimensional cell with the fluid flow taken into consideration and requires only tens of minutes of central processing unit time on engineering workstations. Four sample calculations are presented in this work to provide rigorous validation of the developed simulator. The simulator is capable of predicting the transient behavior of the acid concentration, the porosity of the electrodes, and the state of charge of the battery during discharge, rest, and charge cycles. The model can also be used to investigate the effects of various system parameters, such as electrode dimensions, separator design, temperature, and electrolyte composition on the battery performance (voltage, power, cold cranking amperage, etc.).