A novel hybrid damping scheme was proposed to control the longitudinal motion response at the girder ends during train passage on a railway suspension bridge，utilized multiple types of dampers to control girder-end displacements to meet diverse vibration reduction requirements. With a long-span railway suspension bridge under construction as the engineering background， a detailed spatial truss model and an equivalent single beam simplified model were established. The study systematically investigates the influence of different damper parameters in the hybrid damping scheme on motion control effectiveness. The proposed solution involves installing low-exponent fluid viscous dampers longitudinally between the bridge tower and the stiffening girder. Simultaneously， eddy current dampers are installed longitudinally between the bridge abutment and the stiffening girder. Considering the unique characteristics of the bridge abutment structure， the eddy current dampers are designed as devices capable of withstanding only compressive loads and validated through prototype testing. To further enhance damping performance， the eddy current dampers are equipped with a friction energy dissipation component. This hybrid damping solution effectively controls the longitudinal motion response at the girder ends during train passage， significantly improving the safety and durability of bridge structures. The findings have significant reference value and practical implications for similar engineering projects.