Suppression of spiral waves and spatiotemporal chaos are considered based on the LuoRud91model. We apply local feedback to suppress spiral wave and spatiotemporal chaos. Two control strategies are proposed, namely the static and the moving control methods. It is found that when related parameters are properly chosen spiral wave can be suppressed by static controller, whereas spatiotemporal chaos cannot be suppressed effectively. However, spiral wave and spatiotemporal chaos can be suppressed effectively by moving controller. The corresponding control speed depends on the traveling speed of controller. Spiral wave and spatiotemporal chaos can be suppressed in a short time when the control parameters are suitably chosen.