The invention discloses a steel rail damping fastener used for a depot line of a metro depot. The steel rail damping fastener comprises a base, a base plate under a plate, a vibration insulation cushion, a floating iron base plate and a lateral displacement constraint layer. The base is arranged on a rail bearing. The base plate under the plate is clamped between a base iron base plate and the rail bearing. The vibration insulation cushion is clamped between the base iron base plate and the base plate under the plate and arranged to be like a Chinese character 'zhong' and extends out of a cavity arranged to be like the Chinese character 'zhong'. The floating iron base plate is arranged on the base. The lateral displacement constraint layer is clamped between the side wall of the floating iron base plate and a blocking shoulder. The floating iron base plate is floated by the vibration insulation cushion and the lateral displacement constraint layer, namely the floating iron base plate does not make contact with the base iron base plate. The steel rail damping fastener can constrain transverse movement and vertical movement of a steel rail, namely the vibration insulation cushion constrains the vertical buffering capacity of the steel rail, and the lateral displacement constraint layer limits transverse movement of a railhead. The mutual influence of the two constraints is low, and the rigidity values, in the two directions, of the fastener can be independently designed according to actual requirements, so that the good vibration insulation is achieved under the condition that traveling safety is guaranteed.