The invention discloses a swaying traction system and method for platforms. The swaying traction system comprises a truss platform arranged vertically, a derrick penetrating through the truss platform in the longitudinal direction, a guide traction system arranged on an upper platform of the truss platform, winding drum drive systems driven by an electric motor and four stable systems arranged on a lower platform of the truss platform; coordinate axes XYZ are established on the basis of the center of the derrick, and the XYZ central planes of the derrick overlap with the XYZ central planes of the truss platform in initial setting; steel wire ropes form a traction circulation system, and the upper platform is provided with the winding drum drive systems driving the steel wire ropes to synchronously move in one or two axial directions of the X axis or the Y axis of the local coordinate system XOY. By arranging the stable systems, the derrick can bear certain tension, can be operated smoothly in the swaying process and does not shake. The swaying traction system and method for the platforms have the beneficial effects that the structure is simple, the work space is large and the practical engineering application value is high.