A blade made of composite material including an airfoil formed of filaments or fibers, optionally woven, impregnated with a heat-curable resin, with an intrados wall and an extrados wall between the leading edge and the trailing edge; and a device for damping the vibrations incorporated in one or other of the intrados and extrados walls is disclosed. The damping device is formed of at least one layer made of viscoelastic material and a layer made of rigid material, these layers being superposed. The layer made of rigid material includes a first zone and a second zone. The layer made of viscoelastic material is interposed between the airfoil and the first zone of the rigid layer, and the second zone of the rigid layer is attached to the wall of the airfoil without interposition of viscoelastic material.