In order to improve the security of image encryption and increase the information hiding capacity of encrypted images， a reversible information hiding algorithm based on pixel prediction and secret image sharing was proposed. Firstly， the shared matrix was used to process an image line-by-line and save it into four shared images. Secondly， random key-encrypted shared images were generated using a 2D chaotic mapping. Thirdly， the Median Edge Detector （MED） was used to predict the pixel value of the embedded position in the shared image. The predicted value was aligned to the same bits as the original pixel from the high bit， and the label value was recorded according to the rule. The high three bits of the reference pixel were stored into the embeddable bits. Finally， the label value was stored in the high bits of the reference pixel， and the remaining embeddable bits were the embedding capacity of the proposed algorithm. Experimental results show that the proposed algorithm can provide large capacity embedding space for information hiding， realize the reversible data hiding and the lossless recovery of encrypted images according to the （k，n） threshold strategy.