As an interesting technique that allows data extraction and image recovery without any loss, reversible data hiding in encrypted images is an area of great concern in the field of information security. In this paper, a new reversible data hiding method with high embedding capacity is proposed based on hybrid prediction and Huffman coding. The combination of two embedding mechanisms is innovatively designed to improve the embedding capacity according to different parts of the original image, i.e., the most significant bit-plane and the remaining seven bit-planes. In the first part of this method, the prediction value of each pixel is obtained by calculating the average value of its two neighboring pixels, and all of the most significant bits can be vacated to accommodate additional data. In the second part, the prediction value of each pixel is calculated using the median edge detector predictor, on which the tag map is built. Then, Huffman coding is used to compress the tag map so that a large amount of vacant space is obtained. Finally, the secret data can be embedded into the vacated space by directly using bit substitution. Compared with some recently reported methods, experimental results and analysis have demonstrated that an original image with high visual symmetry/quality can be recovered. Also, larger embedding capacity can be achieved, such as 3.3894 bpp and 3.2824 bpp, for BOSSBase and BOWS2 databases, respectively.