Many low-light enhancement methods ignore intensive noise in original images. As a result, they often simultaneously enhance the noise as well. Furthermore, extra denoising procedures adopted by most methods ruin the details. In this paper, we introduce a joint low-light enhancement and denoising strategy, aimed at obtaining well-enhanced low-light images while getting rid of the inherent noise issue simultaneously. The proposed method performs Retinex model based decomposition in a successive sequence, which sequentially estimates a piece-wise smoothed illumination and a noise-suppressed reflectance. After getting the illumination and reflectance map, we adjust the illumination layer and generate our enhancement result. In this noise-suppressed sequential decomposition process we enforce the spatial smoothness on each component and skillfully make use of weight matrices to suppress the noise and improve the contrast. Results of extensive experiments demonstrate the effectiveness and practicability of our method. It performs well for a wide variety of images, and achieves better or comparable quality compared with the state-of-the-art methods.