We numerically demonstrate acoustophoretic separation of spherical solid particles in air by means of an acoustic Fresnel lens. Beside gravitational and drag forces, freely-falling millimeter-size particles experience large acoustic radiation forces around the focus of the lens, where interplay of forces lead to differentiation of particle trajectories with respect to either size or material properties. Due to the strong acoustic field at the focus, radiation force can divert particles with source intensities significantly smaller than those required for acoustic levitation in a standing field. When the lens is designed to have a focal length of 100 mm at 25 kHz, finite-element method simulations reveal a sharp focus with a full-width at half-maximum of 0.5 wavelenghts and a field enhancement of 18 dB. Through numerical calculation of forces and simulation of particle trajectories, we demonstrate size-based separation of acrylic particles at a source sound pressure level of 153 dB such that particles with diameters larger than 0.5 mm are admitted into the central hole, whereas smaller particles are rejected. Besides, efficient separation of particles with similar acoustic properties such as polyethylene, polystyrene and acrylic particles of the same size is also demonstrated.