Spiral waves are though to be the underlying mechanism of re-entrant ventricular and atrial tachycardias. In such cases, one is generally interested in eliminating spiral wave activity from the medium. In this paper, solve a cubic FitzHugh-Nagumo system of PDEs is solved in two dimensions with initial conditions such that a spiral wave is formed at the center of a rectangular grid. Then the effect of a spatially-localized step-like periodic forcing placed at different positions around the spiral tip is studied. Due to this forcing, the tip begins to drift away from the perturbation in a direction that depends on their relative location. By shifting successively the location of the perturbation relative to that of the tip strategy is developed which it is possible to pursuit the spiral wave away from the center of the grid accelerating its drift with every shift of the perturbation.