A synthetic-grass covering, usable, for example, for making artificial pitches for sports activities, consisting of a substrate made of sheet material and filiform formations, implanted in the sheet material so as to present a looped part that extends up against one of the surfaces of the sheet material and lateral branches that extend in order to simulate the grassy sward of natural turf from the opposite surface of the sheet material. The substrate made of sheet material comprises a pad with coupled thereto a layer made of heat-meltable material, and the filiform formations are also made of heat-meltable material, with the aforesaid looped parts that extend in an area corresponding to the layer made of heat-meltable material, heat-welded to the aforesaid layer.