An augmented reality (AR) system involving the electrically tunable location of a projected image is implemented using a liquid-crystal (LC) lens. The projected image is either real or virtual. By effectively doubling the LC lens power following light reflection, the position of a projected virtual image can be made to vary from 42 to 360 cm, while the tunable range for a projected real image is from 27 to 52 cm on the opposite side. The optical principle of the AR system is introduced and could be further developed for other tunable focusing lenses, even those with a lower lens power. The benefits of this study could be extended to head-mounted display systems for vision correction or vision compensation. We believe that tunable focusing LC optical elements are promising developments in the thriving field of AR applications.