Although a large number of methods have been proposed for low-light image enhancement, there still remain challenges for these methods to simultaneously achieve excellent sharpness/resolution, high calculation efficiency as well as visual pleasure requirements. In this communication, we propose a new low-light image enhancement method based on the degradation model to overcome this dilemma. Specifically, we regard the low-light image enhancement as a special inverse problem of image degradation, and then the task of low-light enhancement is logically embedded in the iterative back-projection (IBP) framework. Meanwhile, an adaptive gamma correction is utilized to adaptively adjust the brightness, and then the IBP framework is transferred to the logarithmic domain instead of the spatial domain for further acceleration. Besides, a simple and effective pre-processing strategy is proposed to pre-enhance the low-light input while making the enhanced image clarify (or visual pleasure). Extensive experimental results on public databases and seven state-of-the-art benchmarks consistently demonstrate the effectiveness and efficiency of the proposed method both visually and quantitatively.