The invention discloses a single-degree-of-freedom damper with adjustable rigidity. The damper comprises a hexahedral air cavity shell, six piston rods, six dielectric elastic films and two eddy current dampers, wherein six through holes are respectively formed in the middle of all faces of the air cavity shell, and the six dielectric elastic films are respectively arranged at all the through holes in a sealing way; the air cavity shell is internally filled with compressed air; the six piston rods are arranged to just face the six through holes; one end of each piston rod is closely jointed and fixedly connected with the corresponding dielectric elastic film; center shafts of the piston rods are collinear with central axes of the corresponding through holes; the ends, far away from the through holes, of the piston rods arranged on the top and at the bottom are connected with the ends, far away from the through holes, of the piston rods arranged on the side faces; the two eddy current dampers are respectively installed at the sides, close to the through holes, of the piston rods arranged on the top and at the bottom; the piston rods arranged on the top and at the bottom are respectively arranged in the centers of the corresponding eddy current dampers in a penetrating way. The single-degree-of-freedom damper with adjustable rigidity can reduce the rigidity of an air spring, andrealizes the adjustable rigidity.