A polarized liquid crystal (LC) lens composed of a LC layers as a polarization switch and a liquid crystal and polymer composites lens (LCPC lens) is demonstrated with electrically switching (ES) mode and optically rewritten (ORW) mode. The lens power of LCPC lens is related to a polarization state of light modulated by the LC layer whose orientations are manipulated either electrically or optically. As a result, the LC lens is not only electrically switchable, but also optically rewritable. Each mode, ES mode or ORW mode, exhibits two discrete lens powers (-1.39 Diopter and +0.7 Diopter). The demonstrated aperture size is 10 mm. The detail optical mechanism is also discussed. The Modulation Transfer Function (so-called MTF) of the lens is measured as well. In addition, the image performance and the dispersion of the LC lens are investigated. Such a polarized LC lens could be a special switch in optical systems due to dual operation modes.