A screw damper and floating slab track system. The screw damper and floating slab track system comprises a floating track slab (1) and screw dampers (2) for supporting the floating track slab (1). Each screw damper (2) comprises a threaded ferrule (21) and an inner elastic barrel. The threaded ferrule (21) supports the floating track slab (1) and is provided with an internal thread. The inner elastic barrel is disposed on a foundation (4) and is provided with an elastic member (23) and a bolt height adjustment member (22). The elastic member (23) is disposed below the bolt height adjustment member (22) and elastically supports the bolt height adjustment member (22). The bolt height adjustment member (22) is provided with an external thread in screw fit with the internal thread of the threaded ferrule (21), the screw fit depth of the inner elastic barrel in the threaded ferrule (21) is adjusted by rotating the bolt height adjustment member (22) or the inner elastic barrel, so as to implement stepless adjustment of the jacking and supporting height of the screw damper (2) to the floating track slab (1). The floating track slab (1) can rapidly and accurately complete leveling and jacking actions, so as to easily, rapidly and accurately implement stepless adjustment of the height; the screw damper and floating slab track system has quite remarkable economic benefits and project benefits and has broad application and popularization prospects. Also provided are a mounting method and a mounting device matching the screw damper and floating slab track system.