Abstract A three-dimensional numerical calculation for analyzing reorientation in liquid crystal (LC) directors and optical phase retardation in an LC lens, which exhibits a tunable conical lens property, is developed. The proposed LC lens design employs a circular electrode, ring electrodes, and a circularly hole-patterned electrode employing a highly-resistive layer in a flat nematic cell. The three-dimensional tilt and azimuthal angle distributions are calculated. Subsequently, the conical phase retardation in the lens region can be estimated. The experimental results obtained for the optical phase profile agree well with the numerically calculated results.