A novel liquid crystal (LC) lens with an on-line tunability on focus length and optical axis is proposed in this study. The designed lens has a LC layer sandwiched by two ITO glasses, one of which is patterned with three sector electrodes. With varied sets of pre-designed voltages applied to these three electrodes, the LC lens can not only render focusing effects but also tunability on the optical axis of the lens to an arbitrary axis. A vector-form equation is developed to predict the direction of axis tuning. Simulations are next conducted to predict dynamics of the LCs in the lens and also the focusing and axis-tuning properties of the lens. Important sizes and materials and fabrication process of the lens are determined and optimized based on simulation results. The designed LC lens is fabricated, and then experiments are conducted to demonstrate the performance of the designed LC lens on axis tuning. It shows that the focusing axis of the LC lens can be effectively changed by pre-calculated combinations of three voltages. It is also shown that the average movement of the focal point per applied voltage reaches 4.778 lm/V.