To achieve a high embedding capacity (EC) without any distortion in the directly decrypted result, a reversible data hiding in encrypted images (RDH-EI) scheme based on full bit-plane compression (FBPC) is proposed. FBPC is designed to vacate as much room as possible before image encryption. To enrich the adjacent redundancy within the most significant bit (MSB) planes, we use flip prediction on the first MSB and then replace the other MSB planes with the XOR result between that plane and its higher level one successively. Hilbert curve scanning is introduced to reduce the dimensionality of the planes to obtain eight highly redundant bit sequences. Huffman coding is then utilizing to compress the bit sequences. After FBPC, a compressed image is obtained. Stream cipher with self-feedback is adapted to encrypt the image. Additional data could be embedded into the reserved space of the encrypted domain. Compared with existing RDH-EI algorithms, the proposed scheme could have a higher EC with no distortion in the directly decrypted image due to the high compression performance of FBPC. Experimental results on the BOWS-2 and BOSSbass datasets demonstrate that the average EC can reach 3.56 and 3.71 bits per pixel, respectively.