The noise and vibration effects of rails can have a significant impact on the environment surrounding the railways. Rail dampers are elements that are attached to the sides of the rail and can improve the track decay rate of rail and then enhance the rails' ability to attenuate noises and vibrations. However, in practical applications, the most efficient rail damper design still cannot adjust its own parameters to adapt to different requirements because their stiffness and damping are fixed after designed. In this work, a tunable magnetorheological elastomer rail damper that works on the principle of a dynamic vibration absorber has been designed, analysed, characterised, and experimentally tested for the suppression of railway noise and vibration. The new rail damper incorporates variable stiffness magnetorheological elastomer layers, whose stiffness can be controlled by an externally applied magnetic field, to realise adaptive characteristics. Experimental characterisations of the magnetorheological elastomer rail damper were performed with an electromagnetic shaker. Subsequently, theoretical predictions of the track decay rate of a UIC-60 rail with different rail dampers and without rail damper were conducted; simulation results verified that magnetorheological elastomer rail dampers can improve the track decay rate of rail over a wider frequency range compared to conventional rail dampers and thus the performance of the magnetorheological elastomer rail damper outperforms other conventional rail dampers on rail noise reduction.