A point cloud obtained by stereo matching algorithm or three-dimensional (3D) scanner generally contains much complex noise, which will affect the accuracy of subsequent surface reconstruction or visualization processing. To eliminate the complex noise, a new regularization algorithm for denoising was proposed. In view of the fact that 3D point clouds have low-dimensional structures, a statistical low-dimensional manifold (SLDM) model was established. By regularizing its dimensions, the denoising problem of the point cloud was expressed as an optimization problem based on the geometric constraints of the regularization term of the manifold. A low-dimensional smooth manifold model was constructed by discrete sampling, and solved by means of a statistical method and an alternating iterative method. The performance of the denoising algorithm was quantitatively evaluated from three aspects, i.e., the signal-to-noise ratio (SNR), mean square error (MSE) and structural similarity (SSIM). Analysis and comparison of performance showed that compared with the algebraic point-set surface (APSS), non-local denoising (NLD) and feature graph learning (FGL) algorithms, the mean SNR of the point cloud denoised using the proposed method increased by 1.22 DB, 1.81 DB and 1.20 DB, respectively, its mean MSE decreased by 0.096, 0.086 and 0.076, respectively, and its mean SSIM decreased by 0.023, 0.022 and 0.020, respectively, which shows that the proposed method is more effective in eliminating Gaussian noise and Laplace noise in common point clouds. The application cases showed that the proposed algorithm can retain the geometric feature information of point clouds while eliminating complex noise.