Low-contrast image enhancement is essential for high-quality image display and other visual applications. However, it is a challenging task as the enhancement is expected to increase the visibility of an image while maintaining its naturalness. In this paper, the weighted histogram equalization using the entropy of the probability density function is proposed. The computation of the local mapping functions utilizes the relationship between non-height bin and height bin distributions. Finally, the complete tone mapping function is produced by concatenating local mapping functions. Computer simulation results on the CSIQ dataset demonstrate that the proposed method produces images with higher visibility and visual quality, which outperforms traditional and recently proposed contrast enhancement algorithms methods in qualitative and quantitative metrics.