This research work is devoted to the problem of excessive vertical vibrations that short to medium-span railway bridges may experiment due to resonance phenomena. A new alternative based on externally increasing the overall damping of the structure by retrofitting the deck with fluid-viscous dampers is proposed in order to reduce detrimental levels of transverse acceleration to admissible ones. This solution could substitute a classical strengthening process or even the complete demolition and replacement of the deck in existing structures under new traffic requirements such as an increase in the speed of the line. A particular configuration of the retrofitting system is proposed which allows the transformation of the vertical oscillations that the deck experiments under the circulation of the railway vehicles into elongation rates of the devices, leading to energy dissipation and the subsequent reduction of the super-structure resonant response. The proposed system could be installed in the original structure and maintained without interfering with everyday traffic.