Nucleation and growth kinetics of dimer-adatom-stacking-fault (DAS) structures on laser-quenched Si(111) surfaces have been investigated for the first time by measuring the time evolution of DAS domain size distribution at 320-440℃ with a scanning tunneling microscope (STM). Time evolution of the distribution suggests two different kinetics of DAS reconstruction. At the very early stage (immediately after laser irradiation), the surface contains many voids and formation of DAS structures is quite rapid. In the next stage (after the disappearance of the voids), the DAS domains develop at constant nucleation and growth rates in a measurable time scale. The temperature dependence of nucleation and growth rates is discussed based on a typical theory of two-dimensional structural phase transition.