Currently, mainstream 3D steganographic algorithms embed data through geometric modifications. To enhance the anti-steganalysis ability of such algorithms, we propose an additive Gaussian noise model for 3D mesh steganography. Our work starts with a theoretical analysis for correlations of vertex coordinate components. Based on this analysis, the whole embedding operation is decomposed into three independent tasks that target three vertex coordinate components, respectively. To obtain vertex-changing probabilities, we construct a payload-limited sender (PLS) problem aimed at minimizing the Kullback-Leibler divergence between the cover and stego mesh distributions for a given payload. Next, vertex coordinates are quantified so that the PLS problem can be solved in practice. Finally, a ternary embedding scheme is taken as a typical steganographic case. Although the proposed Gaussian model is simple and idealized, the experimental results demonstrate that our algorithm possesses the adaptivity and can achieve better anti-steganalysis performance at low payloads than most modern high-capacity 3D mesh steganography based on the geometric modification.