We demonstrate a liquid crystal Fresnel lens (LCFL) with a surface relief structure which has the binary switching property and the merit of low voltage driving. The surface relief structure is fabricated by photopolymerization of a polymer-precursor initiated by ultra-violet light onto a solid cylindrical Fresnel lens with desired optical power. A liquid crystal (LC) layer is sandwiched between a pair of polymer Fresnel lens deposited with planar alignment layers with orthogonal rubbing directions. The ordinary refractive index of LC is chose to be close to the refractive index of the polymer. At voltage-off state, when the polarization of light is parallel to the long axis of LC molecules, the refractive index mismatch of liquid crystals and polymer Fresnel lens enables the focusing of LCFL. At voltage-on state, the LCFL is a slab with homogenous refractive index because of the index matching between LC and polymer. With the benefit of twisted nematic structure, the voltage requirement is significantly low (~6V) for LCFL. The low-voltage binary beam shaping of laser and magnifying lens function using LCFL are experimentally demonstrated in this paper. Polarization-independent LCFL is achievable with a double-layered approach.