For texture patterns distributed on the curved surfaces of objects, it is often necessary to extract and flatten the texture patterns from the curved surfaces for the purpose of comprehensive display and subsequent usage. Therefore, we suggest a curved texture flattening scheme based on the light field camera, especially the focused light field camera, which can provide a high-resolution texture image and corresponding depth map without additional registrations. A curved texture flattening algorithm is designed for this scheme. The algorithm divides the curved texture image into multiple overlapping local texture images, corrects the local texture distortion based on the normal vector of the fitted plane for each local texture image, and finally stitches the corrected local texture images into a completely flattened texture image. Simulated and real experiments reveal that the proposed curved texture flattening algorithm can effectively flatten a variety of texture patterns distributed on different curved surfaces, and the algorithm has certain robustness on the different image quality of texture images and the errors of the depth measurements.