The invention discloses a horizontal elastic damping system of a long-span bridge. The horizontal elastic damping system comprises an elastic seismic-reduction support and common supports, wherein the elastic seismic-reduction support and the common supports are installed between an abutment and a bridge body. Two sides of the elastic seismic-reduction support are provided with the common supports, and the elastic seismic-reduction support mainly consists of an upper support plate, a middle lining plate, a lower support plate and a base. The middle lining plate is assembled between the upper support plate and the lower support plate and forms a curved surface slide fitting surface with the upper support plate and the lower support plate, the base is located under the lower support plate, and a vertical spring is arranged between the lower support plate and the base. The horizontal elastic damping system is simple in structure and reasonable in design, can convert horizontal force suffered by the bridge body into vertical force and convert horizontal damping rigidity of the bridge body into vertical damping rigidity, avoids overlarge horizontal displacement of the bridge body, accordingly limits the horizontal displacement of the bridge effectively, has energy-dissipation and seismic-reduction effects on seismic load and improves the seismic resistance and reduction performance of the bridge.