The invention provides an assembled concrete stair gentle platform beam and slab and a construction method thereof, and belongs to the technical field of civil engineering. The stair gentle platform slab is in a form of a suspension slab, and the gentle beam is used as a supporting seat of the suspension slab; the concrete stair gentle platform beam and the gentle platform slab are integrally prefabricated and mounted, so that the problems such as difficulty in construction of the concrete stair gentle platform beam and slab, increasing of processes and low appearance quality can be solved; the assembling rate of the concrete building construction is increased; and meanwhile, the prefabrication is simple, and the efficiency is high; the construction cost is low, and moreover, the appearance quality is high; outward extending reinforced steel bars at the end of the prefabricated gentle platform beam are removed; a method of arranging a mechanical reinforced steel bar connecting straightthread sleeve at the end of the prefabricated gentle platform beam is carried out to connect inner longitudinal ribs of the stair gentle platform beam and reinforced steel bar sections which are connected in the outer part of the stair gentle platform beam in later period and extend into the supporting seat. The assembled concrete stair gentle platform beam and slab is applicable to the working condition that a vertical component of the supporting seat of the stair gentle platform beam is a cast-in-place concrete component and the working condition that a vertical part of the supporting platform of the stair gentle platform beam is a prefabricated concrete component.