In recent years, flexible liquid crystal displays (LCDs) have attracted much attention due to their thin and lightweight designs, as well as their ease of installation compared with conventional flat-panel LCDs. Most LCDs require backlight units (BLUs) to yield high-quality images. However, the luminance uniformity of flexible BLUs is drastically reduced in the curved state, as the light emitted from a typical BLU is mainly directed in the normal direction. Conventional BLUs do not provide the image quality of flexible BLUs due to uneven luminance distribution from the perspective of the observer. To overcome these issues, here we introduce a novel oblique-angled notched film for improved light distribution of a conventional BLU. The notched structure of the proposed film exhibits V-shaped split behavior during curvature. This elastic deformation is expected to compensate for the spatial luminance of the light emitted from the BLU. We investigated the design requirements for the proposed film based on geometrical calculations. The luminance distribution of a flexible BLU was then simulated using the proposed film, based on geometrical optics theory. The simulation results confirmed that the direction of travel of the light is controllable according to the total internal reflection of the proposed film, thus improving the luminance uniformity of the BLU in a convex-curved state. Based on these results, the proposed approach is expected to improve the luminance uniformity of convex-curved flexible LCDs.