Retinex theory deals with compensation for illumination effects in images, which is usually an ill-posed problem. The existence of noises may severely challenge the performance of Retinex algorithms. Therefore, the main aim of this paper is to present a general variational Retinex model to effectively and robustly restore images corrupted by both noises and intensity inhomogeneities. Our strategy is to simultaneously recover the noise-free image and decompose it into reflectance and illumination component. The proposed model can be solved efficiently using the Alternating Direction Method of Multiplier (ADMM). Numerous experiments are conducted to demonstrate the advantages of the proposed model with Retinex illusions and medical image bias field correction for images in presence of Gaussian noise or impulsive noise.