In this work, we present a one-dimensional model for the discharge behavior of lithium-sulfur (Li-S) batteries. In addition to the consideration of multiple-step polysulfide dissolution and reductions, the surface nucleation and growth kinetics coupled with electrochemical reactions is particularly exploited for describing the Li2S precipitation. Unlike previous models that overlook the rate-dependent precipitation phenomenon, our model reveals that discrete Li2S particle growth becomes suppressed at higher rates, resulting in smaller Li2S precipitates with a more uniform particle size distribution and a limited discharge capacity. Experimental discharge curves and discharge product observation adequately confirm our numerical results. It is further predicted that promoting the growth of Li2S particles, including lowering the initial nucleation rate and providing a suitable amount of initial nucleation sites, can efficiently prolong the Li-S battery's discharge capacity.