Retinex theory deals with compensation for illumination effects in images, which has a number of applications including Retinex illusion, medical image intensity inhomogeneity and color image shadow effect etc.. Such ill-posed problem has been studied by researchers for decades. However, most exiting methods paid little attention to the noises contained in the images and lost effectiveness when the noises increase. The main aim of this paper is to present a general Retinex model to effectively and robustly restore images degenerated by both illusion and noises. We propose a novel variational model by incorporating appropriate regularization technique for the reflectance component and illumination component accordingly. Although the proposed model is non-convex, we prove the existence of the minimizers theoretically. Furthermore, we design a fast and efficient alternating minimization algorithm for the proposed model, where all subproblems have the closed-form solutions. Applications of the algorithm to various gray images and color images with noises of different distributions yield promising results.