•We propose a novel data hiding technique using adaptive difference recovery (ADR).•We design an efficient RDHEI method using the ADR-based technique.•The proposed RDHEI method outperforms some state-of-the-art RDHEI methods in payload. Vacating room after encryption (VRAE) is a popular framework of reversible data hiding for encrypted images (RDHEI). Most VRAE based RDHEI methods do not make a desirable payload. To address this issue, this paper proposes a novel data hiding technique using adaptive difference recovery (ADR) and exploits this novel technique to design an efficient VRAE based RDHEI method. Specifically, the proposed ADR-based data hiding technique adaptively determines the range of original difference between a cover pixel and a reference pixel with correlation according to the marked difference generated by bit substitution technique. The cover pixel can be recovered losslessly with the range of original difference and the reference pixel. In the proposed RDHEI method, the encrypted image is generated by block permutation and block-based modulation so that spatial redundancy within encrypted image blocks is preserved. Then the ADR-based data hiding technique is applied to the encrypted blocks. Experiment results show that the proposed RDHEI method outperforms some state-of-the-art RDHEI methods in payload. The average embedding rates of the proposed RDHEI method on the BOSSbase, BOWS-2 and UCID datasets are 3.2045, 3.1145 and 2.4633 bpp, respectively.