This study presents a lossless robust data hiding scheme based on significance‐bit‐difference expansion. The original cover image can be recovered without any distortion after the hidden data have been extracted if the stego image remains intact, on the other hand, the hidden data can be robust against unintentional changes applying to the stego image, such as image compression and sometimes unavoidable addition of random noise which is below a certain level and does not change the content of an image. The proposed scheme decomposes pixels in a cover image into two parts, that is, the higher significant bits (HSB) and the least significant bits (LSB), and calculates the HSB difference between adjacent pixels. Bits are embedded into HSBs by shifting the HSB difference value histogram bins. The shift and shifting rule are fixed for all HSB difference values, and reversibility is achieved. Furthermore, owing to the separation of HSBs and LSBs, minor alteration applying to the stego image generated by non‐malicious attacks such as Joint Photographic Experts Group (JPEG) compression, which will not change the HSB values as well as the HSB difference values, and robustness is achieved. Experimental results show that, compared with previous works, the performance of the proposed scheme is significantly improved.