Based on the method of the free energy density functional, the effect of grain boundaries on the precipitation process in binary alloys is considered. A comparative analysis of precipitation kinetics has been carried out for a single-crystal fragment of a solid solution and for a fragment containing a part of the boundary between two grains. We have found the influence of grain boundaries on the kinetics of the average radius of precipitates, their concentration, and nucleation rate for several compositions of the alloy.