A partially prefabricated reinforced concrete anti-seismic staircase and its construction method. The staircase consists of a lower stair section board, an upper stair section board, a lower platform board, an upper platform board, a platform frame, a polytetrafluoroethylene board, a floor platform board, a platform beam, and a sealing strip , frame beams, connecting beams and frame columns, in which the platform frame is a prefabricated reinforced concrete member; the lower stair slab and the lower platform slab are integrally poured, and the upper stair slab and the upper platform slab are integrally poured; the lower platform slab and the upper platform slab are both Riding on the platform frame, there are two layers of polytetrafluoroethylene boards between the upper platform board and the platform frame; there is a gap between the lower platform board and the upper platform board. In the construction of the stairs, the platform frame is prefabricated first, a layer of polytetrafluoroethylene board is fixed on the platform frame, and the lower stair slab, the lower platform slab and the structural components of the lower floor are poured at the same time, and then the upper stair slab, upper platform slab and upper structural members. The invention can reduce the shock damage of the stairs without affecting the shock resistance of the main structure.