In order to improve the embedding capacity of reversible data hiding in encrypted images, a reversible data hiding algorithm in encrypted images based on adaptive median edge detection (AMED) and Huffman coding was proposed. In the proposed algorithm, the cover image was first subjected to block-level expansion. Subsequently, the adaptive parameters were introduced during the prediction phase to propose an optimization scheme for median edge detection (MED), where parameters vary with image texture features to enhance pixel prediction accuracy. Finally, the most significant bits (MSB) of pixels were marked, and the marked results were compressed using Huffman coding to free up space for embedding secret data. Experimental results demonstrated that the algorithm could accurately extract secret data while ensuring reversibility. Moreover, compared to existing algorithms, the embedding capacity had been increased, with an average embedding rate reaching as high as 2.632 0 bits per pixel (bpp).