This study is dedicated to the design of a new negative liquid crystal (LC) lens with multiple ring electrodes in unequal widths. The number and widths of the multiple ring electrodes are designed to offer online tunability on focusing length by predetermined individual electrode voltages. This aims to render a smooth refraction index distribution that mimics well a divergent lens based on the theory of a gradient refraction index (GRIN) lens. Finally, the proposed negative LC lens is fabricated with the capability of realizing different focus lengths in a relatively large aperture of 5 mm and a thickness of 0.7 mm. Experiments are conducted to verify expected light-diverging performance. The effective focus length (EFL) is measured based on interference patterns. It is shown that the proposed negative LC lens is able to realize light-divergent effects with an EFL as short as 357.9 mm.