Support vector machine (SVM) is a popular machine learning technique and its variant least squares support vector regression (LS-SVR) is effective for image denoising. However, conventional LS-SVR does not fully consider the sampling distribution of noisy images, which may degrade the performance of the algorithm. In this paper, we propose a new fuzzy density weight SVR (FDW-SVR) denoising algorithm, which assigns fuzzy priority to each sample according to its density weight. FDW is designed to estimate the joint probability density function via the fuzzy theory based on the pixel density and neighborhood density. Extensive experimental results show that FDW-SVR is superior to those state-of-the-art denoising techniques in light of both subjective and objective evaluations.