The transmission and storage of massive 3D models in cloud space offer significant convenience to human life, however, they also pose significant security threats. To address this, we propose a large-capacity Reversible data hiding in the encrypted domain (RDH-ED) algorithm for 3D mesh model based on optimal grouping strategy and multiple-bit plane prediction. Firstly, the proposed algorithm utilizes the optimal grouping strategy to group the vertices of the 3D mesh model. Secondly, in each group, a multiple-bit plane prediction algorithm is employed to vacate redundant rooms for embedding secret data. Finally, the receiver uses the embedded flag bit and length label within the group to achieve lossless model recovery. Experimental results demonstrate that the proposed algorithm is completely reversible, with a secret data extraction error rate of 0, and exhibits a higher embedding capacity compared to existing algorithms.