A thin planar acoustic lens composed of concentric annular slits on a circular steel plate covered by a membrane made up of aluminum foil is numerically designed, and its performance in focusing low-frequency sound in air is experimentally demonstrated. Resonant fundamental modes of the membrane-backed cavities are calculated via the Finite-Element Method. By carefully adjusting the radii of the concentric cavities, the phase discontinuity across the cavities can be employed to achieve constructive interference of sound waves at a focal length of 200 mm, which is close to the acoustic wavelength, at 2190 Hz. The designed lens has an overall radius which is approximately one fourth of the radius of a conventional acoustic Fresnel lens employing a wavelength path length difference between adjacent cavities.