Optical and acoustic tractor beams are currently the focus of intense research due to their counterintuitive property of exerting a pulling force on small scattering objects. In this Letter we propose a matter-wave tractor beam and utilize the de Broglie waves of nonrelativistic matter particles in analogy to "classical" tractor beams. We reveal the presence of the quantum-mechanical pulling force for the variety of quantum mechanical potentials observing the resonant enhancement of the pulling effect under the conditions of the suppressed scattering known as the Ramsauer-Townsend effect. We also derive the sufficient conditions on the scattering potential for the emergence of the pulling force and show that, in particular, a Coulomb scatterer is always shoved, while a Yukawa (screened Coulomb) scatterer can be drawn. Pulling forces in optics, acoustics, quantum mechanics, and classical mechanics are compared, and the matter-wave pulling force is found to have exclusive properties of dragging slow particles in short-range potentials. We envisage that the use of tractor beams could lead to the unprecedented precision in manipulation with atomic-scale quantum objects.