In recent years, reversible data hiding (RDH), a new research hotspot in the field of information security, has been paid more and more attention by researchers. Most of the existing RDH schemes do not fully take it into account that natural image's texture has influence on embedding distortion. The image distortion caused by embedding data in the image's smooth region is much smaller than that in the unsmooth region, essentially, it is because embedding additional data in the smooth region corresponds to fewer invalid shifting pixels (ISPs) in histogram shifting. Thus, we propose a RDH scheme based on the images texture to reduce invalid shifting of pixels in histogram shifting. Specifically, first, a cover image is divided into two sub-images by the checkerboard pattern, and then each sub-image's fluctuation values are calculated. Finally, additional data can be embedded into the region of sub-images with smaller fluctuation value preferentially. The experimental results demonstrate that the proposed method has higher capacity and better stego-image quality than some existing RDH schemes.