This paper presents a high-fidelity reversible data hiding scheme for digital images based on a new prediction strategy called pixel-value-ordering (PVO) and the well-known prediction-error expansion (PEE) technique. Specifically, a host image is first divided into non-overlapped equal-sized blocks. Then the maximum and minimum values of each block are predicted by other pixels of the block according to their pixel value orders. With such a PVO-based predictor, data embedding is implemented via PEE. The incorporation of PVO into PEE has an advantage in reducing the number of shifted pixels, and thus it can alleviate the degradation in image quality. Consequently, the proposed method can embed adequate data into a host image with rather limited distortion. The PSNR of a marked image versus its original one is guaranteed to be above 51.14dB. In addition, a solution is provided to further improve the embedding performance by priorly using the flat blocks to embed data while leaving the rough ones unchanged. We demonstrate the proposed method outperforms some advanced prior arts with abundant experimental results.