The present invention discloses an auto-stereoscopic display and a liquid crystal lens (LC lens) unit. The LC lens unit orderly consists of a concave lens, a birefringence LC convex lens, and a conductive layer from an emitting surface to an incident surface. The birefringence LC convex lens, embedded in the concave lens, has both a ordinary refractive index and a extraordinary refractive index. The conductive layer has a plurality of control electrodes which generate an electric field to adjust an alignment of LC molecules of the birefringence LC convex lens for adjusting the equivalent refractive index of the birefringence LC convex lens to make the equivalent refractive index between the refractive index of the concave lens and the extraordinary refractive index of the birefringence LC convex lens. The aim is to compensate a viewer for a refraction angle of light that the human eye requires when the viewer observes an auto-stereoscopic display with different distances. In addition, the extraordinary refractive index is far larger than ordinary refractive index. Once the LC molecules rotate by a slight angle, the incident polarized light obtains larger refractive index. Thus, a 3D/2D switch is achieved. In other words, a smaller electric field can achieve the target of a 3D/2D switch, which reduces power consumption.