These days, digital images are one of the most profound methods used to represent information. Still, various images are obtained with a low-light effect due to numerous unavoidable reasons. It may be problematic for humans and computer-related applications to perceive and extract valuable information from such images properly. Hence, the observed quality of low-light images should be ameliorated for improved analysis, understanding, and interpretation. Currently, the enhancement of low-light images is a challenging task since various factors, including brightness, contrast, and colors should be considered effectively to produce results with adequate quality. Therefore, a retinex-based multiphase algorithm is developed in this study, in that it computes the illumination image somewhat similar to the single-scale retinex algorithm, takes the logs of both the original and the illumination images, subtract them using a modified approach, the result is then processed by a gamma-corrected sigmoid function and further processed by a normalization function to produce to the final result. The proposed algorithm is tested using natural low-light images, evaluated using specialized metrics, and compared with eight different sophisticated methods. The attained experiential outcomes revealed that the proposed algorithm has delivered the best performances concerning processing speed, perceived quality, and evaluation metrics.