In order to mitigate the longitudinal vibration of the long-span highway suspension bridge under combined wind and traffic loads during normal operation，an analytical platform of wind-traffic-suspension was established by introducing the fluid viscous damper（FVD） into the existing wind-vehicle-bridge coupled dynamic system. Using a typical long-span suspension bridge in mountain area as an engineering background，the established analytical platform was applied to investigate the time-frequency characteristics of the longitudinal vibration of the stiffening girder under stochastic wind and traffic loads. The time-frequency characteristics in the cases with and without implementing the FVD was compared. Subsequently，sensitivity analysis was carried out to study the influence of the FVD on the displacement response of the stiffening girder and the tower bending moment. The response surface method was employed to seek the optimum FVD parameters with the goal to optimize the structural mechanical behaviors and reduce the girder’s longitudinal vibration under stochastic wind and traffic loads. The results indicate that after implementing the FVD，the amplitude of the longitudinal vibration of the stiffening girder under various loading scenarios can be mitigated，while whether the vibration frequency can be reduced depends on the dominant frequencies of the longitudinal vibration. In addition，both the maximum longitudinal displacement and the longitudinal cumulative displacement of the stiffening girder under wind only，traffic only or the combined wind and traffic loading scenarios can be reduced effectively after the mplementation of the FVD，and the performance of the FVD in mitigating the longitudinal vibration increases with larger damping coefficient and smaller velocity exponent. Furthermore，the influence of the FVD on the tower bending moment depends on the loading type and the use of the FVD could enlarge the tower bending moment under wind-only loading scenario. The optimization result shows that the optimum damping coefficient ranges from 500 to 700 kN/（m/s）α，and the optimum velocity exponent ranges from 0.3 to 0.5.