Most high-capacity, 3D data-hiding schemes introduce irreversible changes into the host model. For artistic or technical models, not modifying the original mesh models is sometimes very important. This work describes a novel, multi-layer, reversible data-hiding scheme for 3D mesh models. The proposed scheme starts with finding an independent set of vertices for embedding data. The prediction residues of the vertices and the secret bit string are then encoded using the arithmetic coding method. The embedding procedure is done by substituting part of the mantissa of these vertices with the coded arithmetic decimal numbers. A maximum distortion constraint is set for each embedding vertex, such that the distortion on the cover model is controlled to be imperceptible. Users can construct a multi-layer embedding scheme by repeatedly applying the single-layer embedding procedure until the secret bit string is completely embedded. By integrating the arithmetic encoder and the substitution operation, the proposed method achieves 4-8 bits/vertex embedding capacity while reserving the ability of rebuilding the original model. Experimental results show that the proposed scheme can successfully reconstruct the original model while extracting the secret bit string.