The invention relates to a precast slab type vibration damping rail structural system and a matched construction method. The rail structural system consists of steel rails, fasteners, precast slabs, an elastic cushion layer, a sealing sleeve, a longitudinal connecting device, a filling layer and the like, wherein the elastic cushion layer and the precast slabs can be compounded as a whole in a plant. According to the engineering needs, a track board can be reserved with 1-3 holes (for infusing the filling layer and observing an infusing state) which penetrate through the track board in a thickness direction, pre-formed holes for mounting supporting legs, a hole for mounting a measuring and positioning mark, an aligning mark for laying and positioning, a pre-embedded part for composite connecting of the elastic cushion layer, lifting pins for lifting, a pre-embedded part for longitudinally connecting the track board, a pre-embedded part for mounting a contact rail, and the like. The precast track board is laid by adopting laying equipment such as a plate transporter, a crane trolley, a fine-tuning trolley and the like, so that the precast slab type vibration damping rail structural system has the characteristics of a simple construction process, high construction speed, high construction speed, good rail smoothness and low labor intensity; and the convenience problem of replacing the track board and the elastic cushion layer after operation is solved.