Many algorithms to enhance low-light images have been proposed. They often assume that low-light images are clean. However, images acquired in low-light environments often contain noise. Consequently, those enhancement algorithms often simultaneously amplify the noise. For the purpose of overcoming the above-mentioned shortcoming, we propose a framework of joint enhancement and denoising. It is accomplished using the non-subsampled shearlet transform with adaptive soft-threshold shrinkage. The multi-scale feature of the proposed model can better represent edge textures in an image and decomposes an image into two parts of low frequency and high frequency for separate processing. Experimental results show that, compared with state-of-the-art methods, the proposed algorithm can achieve better quality in terms of objective assessment and subjective assessment.