Focus-tunable liquid lens arrays have been used to improve depth in glass-free three-dimensional devices where high fill factor is required. For high fill factors, polygonal apertures should be used, but due to the difficulty of controlling aberrations during focus tuning, polygonal aperture focus-tunable lenses have rarely been studied. This Letter proposes a new structure with walls at the lens boundaries using a square parabolic lens model to control the quadrafoil aberration induced by the square aperture. ANSYS simulation confirmed that the lens surface was closest to the parabolic lens model when the wall thickness was 1.4 mm. A fabricated lens array demonstrated the quadrafoil inhibitory effect and confirmed the utility of the new structure. (C) 2019 Optical Society of America