The mechanism of destabilization is studied for the rotating vortices (scroll waves and spiral waves) in excitable media induced by a parameter modulation in the form of a travelling-wave.It is found that a rigid rotating spiral in the two-dimensional (2D) system undergoes a synchronized drift along a straight line, and a 3D scroll ring with its filament closed into a circle can be reoriented only if the direction of wave number of a travelling-wave perturbation is parallel to the ring plane.Then, in order to describe the behaviour of the synchronized drift of spiral wave and the reorientation of scroll ring, the approximate formulas are given to exhibit qualitative agreements with the observed results.