Data hiding in encrypted image is a recent popular topic of data security. In this paper, we propose a reversible data hiding algorithm with pixel prediction and additive homomorphism for encrypted image. Specifically, the proposed algorithm applies pixel prediction to the input image for generating a cover image for data embedding, referred to as the preprocessed image. The preprocessed image is then encrypted by additive homomorphism. Secret data is finally embedded into the encrypted image via modular 256 addition. During secret data extraction and image recovery, addition homomorphism and pixel prediction are jointly used. Experimental results demonstrate that the proposed algorithm can accurately recover original image and reach high embedding capacity and good visual quality. Comparisons show that the proposed algorithm outperforms some recent algorithms in embedding capacity and visual quality.