In our previous work, we reported that a droplet of a Belousov-Zhabotinsky (BZ) reaction medium moves in one direction and then in the opposite direction, when a chemical wave propagates spherically inside the droplet. In the present study, we report our new results on the continuous motion of the BZ droplet, i.e., on the rotational and repeated back-and-forth motion when a spiral wave and a scroll ring propagated inside the droplet, respectively.