The domain dynamics of a quenched system with many nonconserved order parameters was investigated by using the time-dependent Ginzburg-Landau kinetic equations. Our computer simulation of a model two-dimensional system produced microstructures remarkably similar to experimental observations of normal grain growth. After a short transient, the average domain or grain radius was found to increase with time as ${\mathit{t}}^{1/2}$, in agreement with most of previous mean-field predictions and more recent Q-state Potts model Monte Carlo simulations.