Geometric type of liquid crystal (LC) lens can be obtained by using the spherical substrate in a liquid crystal cell. The LC lens can have a potential application to a kind of light wave controlling device by utilizing the electronic variable focusing properties. However, it shows a particular aberration properties induced by the molecular orientation related with a curved substrate structure. In this study, LC molecular orientation states in the LC lens and the optical properties are investigated by the experimental and the theoretical approaches. Interference fringe patterns induced by the LC layer are observed and optical path distribution properties are compared between the rubbing direction and the direction perpendicular to the rubbing. One dimensional model is applied to the molecular orientation calculation, and the optical path difference in the 2D area and the wave aberrations are calculated for normal incidence. It is confirmed that a particular wave aberration dependent upon the rubbing direction appears, and the influence of the curved substrate strongly depend upon the thickness of the LC layer. Therefore, the aberration phenomena of the convex and concave lens are quite different even though they have the spherical substrate with the same magnitude of curvature. When a voltage is applied to the LC lens, reverse tilted disclination lines tend to appear and they usually cause a fatal degradation of lens properties. The disclination lines can be eliminated by introducing a small pretilt angle to the alignment layer within a smaller inclination of substrate. However, even in the disclination free state, there is some influence on the wavefront through the LC lens; that is, large inclination of the wave front causes in the lower applied voltage.