Reversible data hiding in encrypted image (RDHEI) can protect the privacy of original image content and enable data owner manages the encrypted image by reversible embedding additional data. In this paper, we propose a novel RDHEI framework based on reversible image reconstruction (RIR). Different from all the previous RDHEI methods that reversible data hiding (RDH) phase are unsatisfactory as the encrypted images hardly contain redundancy space, RIR rearranges the original image to construct a redundancy image and the meaningful information of the original image will become invisible at the same time. This rearranged image will be used as encrypted image, so RDH into this encrypted image becomes very easy and more additional data can be embedded. With RIR, general RDH algorithms for plaintext domain can be employed to realize a RDHEI scheme. Experimental results show that the performance of the proposed RIR based RDHEI schemes outperform the previous similar algorithms.