The invention discloses a spiral spring damper with early rigidity capable of being adjusted. The spiral spring damper is characterized in that a back pressure is arranged between two end plates of the damper, the back pressure device comprises two sets of prepressing steel cables with the number being three or more in each set and two floating pressing plates, wherein each floating pressing plate is arranged on a guide rod between one end plate and a cylindrical spiral compressed spring in a sleeving mode, the two sets of prepressing steel cables are symmetrically distributed on the periphery of the cylindrical spiral compressed spring in a linear state about the axes of the guide rods correspondingly, one ends of each set of prepressing steel cables are fixed to one floating pressing plate, the other ends of each set of prepressing steel cables penetrate through the other floating pressing plate to be anchored to the corresponding end plate adjacent to the floating pressing plate through a steel cable self-locking tensioning anchor gear, the two sets of prepressing steel cables are tensioned, and the cylindrical spiral compressed spring is always clamped between the two floating pressing plates.