Great concern has arisen in the field of reversible data hiding in encrypted images (RDHEI) due to the development of cloud storage and privacy protection. RDHEI is an effective technology that can embed additional data after image encryption, extract additional data without any errors and reconstruct original images losslessly. In this paper, a high-capacity and fully reversible data hiding in encrypted images method based on pixel prediction and multi-MSB (most significant bit) planes rearrangement is proposed. First, we use the median edge detector (MED) predictor to calculate the predicted value. Next, unlike previous methods, in our proposed method, signs of prediction errors (PEs) are represented by one bit plane and absolute value of PEs are represented by other bit planes. Then, we divide bit planes into uniform blocks and non-uniform blocks, and rearrange these blocks. Finally, according to different pixel prediction schemes, we embed different number of additional data adaptively. The experimental results prove that our method has higher embedding capacity compared with state-of-the-art RDHEI methods.