During the discharge process of lithium-sulfur batteries, the nucleation and growth of Li2S precipitates result in a non-uniform Li2S particle size distribution, significantly affecting the charging process. However, a uniform Li2S distribution at the initial state of the charging process of the batteries is assumed in the models reported in the literature, leading to an unrealistic simulation of the charging process. To address this issue, we propose a one-dimensional transient mathematical model, which incorporates the size-dependent Li2S dissolution and redox mediation reaction between dissolved polysulfides and Li2S particles into the charging process. Simulation results show that the dissolution rate of large Li2S particles is suppressed at a lower potential due to the small specific surface area, while the smaller Li2S particles are electrochemically oxidized into dissolved polysulfides first, which further act as the redox mediators to promote the oxidation of larger Li2S particles. Capturing these effects enables an excellent agreement between the predicted and measured charging voltage profiles. Moreover, the effects of particle sizes and redox mediation reaction rates are studied. It is revealed that the optimal amount of smaller-sized Li2S particles and suitable redox mediation reaction rate allow for a lower charging over-potential. Furthermore, it is shown that the effect of redox mediation rates on the dissolution of Li2S large particles exerts a significant influence on the charging process.