In this paper,  the generalized geometric representation of the 3D Point Cloud data was proposed based on Clifford algebra, where the expressions of 3D Point Cloud data were unified without losing their geometric meaning, and the geometric operation was coordinate-free for different dimensional spaces. The Clifford Fourier Transform was introduced into the digital watermarking algorithm for the 3D Point Cloud model, where point cloud models were mapped to the corresponding domain coefficients in space G3. Then the watermark was embedded or extracted based on these coefficients. The experimental results show that the algorithm has very good performance in affine transformation, reordering, simplification and noise, and is robust against attacks.