Transient aerodynamic response of an airfoil to a rapidly deploying spoiler is numerically investigated using a two-dimensional turbulent compressible Navier-Stokes flow model. The spoiler moving relative to a stationary airfoil is treated by an overset grid bounded by a dynamic domain-dividing line, the concept of which is developed first in this paper. The fluid dynamic mechanism of the adverse lift because of the rapidly deploying spoiler is analyzed. Also the effect of spoiler deploying rate on the initial behavior of the aerodynamic response is expounded, which is of interest in view of active control technology and controller design for the spoiler. The results of present computation about the stationary as well as moving spoilers are relatively in good agreement with the existing experimental data.