The dilemma between tunable range of a lens power and an aperture size in gradient-index (GRIN) type of liquid crystal (LC) lenses is well known due to the limitation of birefringence of LC martials and the nature of soft matters. In order to overcome the dilemma of the power law, a multi-layered LC lens was previously proposed by us. However, the aperture size of GRIN LC lenses is still difficult to exceed 10 mm. In this paper, we proposed an electrically tunable GRIN LC lens via nematic liquid crystals with a method of spatially extended phase distribution. A GRIN LC lens with an aperture size of 20 mm is achieved. The proposed GRIN LC lens consists of two LC elements modulating wavefronts at different regions of the lens aperture extending to 20 mm. The lens power of the GRIN LC lens is continuously tunable, while the LC lens can function as a positive lens, a negative lens, and a bifocal lens. The proposed GRIN LC lens not only overcomes the dilemma of the power law but also provides a more practical approach that could benefit the ophthalmic applications and augmented reality systems.