Control of cable-stayed bridge flutter for earthquake and aerodynamic hazard mitigation represents a relatively new area of research. This paper proposes a new optimized smart control system to mitigate the cable-stayed bridge flutter due to seismic and aerodynamic vibration. A Magnetorheological (MR) fluid damper, which belongs to the class of controllable fluid dampers, is proposed for use in a control strategy for mitigating its effect on the cable-stayed bridge. Genetic algorithm is adopted to determine the flutter acceleration levels, and corresponding forces of MR dampers. The optimized forces values from MR dampers are studied under the effect of five strong earthquakes recorded, known as El-Centro, Mexico City, San Fernando, Ker Country, and Northridge earthquakes. The time delay between the monitoring system and the actuator response is also studied. The simulation and optimization results shows that the proposed control strategy using MR dampers is the promising one of the applicable control methods to reduce the seismic and aerodynamic flutter vibration of the stayed bridge.