Transient aerodynamic response of an airfoil to a moving plane-flap is numerically investigated using the two-dimensional Euler equations with conservative Chimera grid method. A body moving relative to a stationary grid is treated by an overset grid bounded by a 'Dynamic Domain Dividing Line' which has an advantage for constructing a well-defined hole-cutting boundary. A conservative Chimera grid method with the dynamic domain-dividing line technique is applied and validated by solving the flowfield around a circular cylinder moving supersonic speed. The unsteady and transient characteristics of the flow solver are also examined by computations of an oscillating airfoil and a ramp pitching airfoil respectively. The transient aerodynamic behavior of an airfoil with a moving plane-flap is analyzed for various flow conditions such as deflecting rate of flap and free stream Mach number.