Growth behavior and kinetics of grains in a liquid matrix has been studied by computer simulation for various physical and processing conditions. The kinetics of growing and dissolving grains were considered to follow those of single crystals in a matrix. Depending on the shape of crystals, rounded or faceted, different kinetic equations were adopted for growing grains and an identical equation for dissolving grains. Effects of such critical parameters as step free energy, temperature, and liquid volume fraction were evaluated.