This work proposes to develop an underwater image enhancement method based on histogram-equalization (HE) approximation using physics-based dichromatic modeling (PDM). Images captured underwater usually suffer from low contrast and color distortions due to light scattering and attenuation. The PDM describes the image formation process, which can be used to restore nature-degraded images, such as underwater images. However, it does not assure that the restored images have good contrast. Thus, we propose approximating the conventional HE based on the PDM to recover the color distortions of underwater images and enhance their contrast through convex optimization. Experimental results demonstrate the proposed method performs favorably against state-of-the-art underwater image restoration approaches.