Excessive cumulative stroke in the longitudinal movement of long-span suspension bridge can led to premature fatigue damage in the bridge's connecting components. However, existing control devices, like viscous damper, remain suboptimal. This paper aims to reveal the underlying mechanism of cumulative stroke control and find an effective control method to address this issue. Firstly, the statistical and frequency characteristics of longitudinal displacement were analyzed based on a 24-hour field measured data set. Secondly, the cumulative stroke control performance of nonlinear viscous damper was evaluated with a SDOF system, uncovering the reasons for their low efficiency in controlling cumulative stroke. Thirdly, the Maxwell-Coulomb friction damper was introduced to control the excessive cumulative stroke, and its effective control performance was validated. Finally, a novel parallel model combining viscous dampers and friction dampers was proposed to leverage the superior performance of friction damper in controlling the cumulative stroke under daily operation condition, while also harnessing the seismic response mitigation capacity of the viscous damper. This research enhances the understanding of cumulative stroke control in long-span suspension bridges and presents an innovative control method by introducing the Maxwell-Coulomb friction damper, highlighting its potential for practical application in bridge engineering.