A liquid crystal (LC) lens array based on polymer protrusion is proposed. The indium tin oxide (ITO) electrodes are coated on periodic polymer protrusion, a dielectric layer is used for flattening phase profile, and the vertical electric field across the LC layer varies linearly over the lens aperture, which is obtained in the voltage-on state. As a result, a centrosymmetric gradient refractive index profile within the LC layer is generated, which causes the focusing behavior. As a result of the optimization, a thin cell gap which greatly reduces the switching time of the LC lens array can be achieved in our design. The main advantages of the proposed LC lens array are in the comparatively low operating voltage, the flat substrate surface, the simple electrodes, and the uniform LC cell gap. The simulation results show that the focal length of the LC lens array can be tuned continuously from infinity to 1.28 mm by changing the applied voltage.