Sensitivity analysis of a mathematical model of a lithium-sulfur (Li-S) battery was performed by investigating the response of the model to variation of the exchange current densities, diffusion coefficients, and cathode thickness over a wide range; the results of the analysis were used to explain the some aspects of the behavior of the system which may be seen in experiments. In particular, among all the exchange current densities, the exchange current density of the elemental sulfur reduction has the most significant effect on the discharge capacity of the cell. The variation of the diffusion coefficients was also analyzed, providing information on the non-uniformity of precipitants in the cell after discharge. An optimum cathode thickness was presented to gain the highest capacity of the cell. Finally, the simulation of charging was studied, showing that the model needs a large solubility product of di-lithium sulfide to be able to simulate the charge process of a cell.