The existing reversible data hiding in encrypted images (RDHEI) methods suffer from insufficient prediction accuracy, limited embedding capacity and excessive auxiliary information overhead; this paper proposed an improved RDHEI algorithm based on multi-directional gradient prediction and global zero-value high bit-plane compression. The proposed method first employed a multi-directional gradient predictor (MDGP) to adaptively fuse gradient information from horizontal, vertical, and diagonal directions, thereby achieving high-precision pixel prediction and reducing prediction errors. Then, the algorithm globally compressed the continuous zero-value high bit-plane of the prediction-error image. Meanwhile, it integrated block rearrangement and efficient coding mechanism, which effectively released the embedding space and reduced the redundancy of auxiliary information. In the embedding and extraction phases, the algorithm supported separate access of the encryption key and the data key to realize the secret information extraction and lossless recovery of the original image respectively. The experimental results show that the proposed method achieves high embedding rate and fully reversible recovery quality on standard test images and public datasets, with average embedding rates of 3.886 bpp, 3.759 bpp, 2.765 bpp and 3.696 bpp on BOSSbase, BOWS-2, Aerials and Miscellaneous datasets respectively. Meanwhile, the entropy of the encrypted image is close to 8 bits/pixel, and the correlation coefficient is close to zero, which demonstrates superior security and stability. This study achieves a coordinated optimization of capacity, reversibility, and security, providing an efficient and feasible new scheme for encrypted image privacy protection and secure communication.