The work aims to propose a new blind algorithm for data hiding of 3D mesh models with complete distortion-free to solve the problem that the current 3D data hiding cannot take into account both distortion-free and blind extraction. First, chaotic logical mapping was used to select embedding and extracting modes to ensure the security of data. Then, the face elements rearrangement that would not cause distortion of the 3D model was adopted. The secret data was embedded by rearranging the triangular face elements through different embedding mode rules. The receiver could extract the secret data according to the corresponding extraction mode rules. Simulation results and analysis indicated that the algorithm did not cause any distortion to the 3D model, the embedding capacity was two bits per vertex, and it could resist affine transformation attacks, noise attacks and smoothing attacks. This blind 3D data hiding algorithm has no distortion, large capacity, high security and strong robustness, and is suitable for situations where the 3D carrier cannot be modified, such as military, medical, secret communication and copyright protection.