Underwater image enhancement aims at improving the visibility and eliminating color distortions of underwater images degraded by light absorption and scattering in water. Recently, retinex variational models show remarkable capacity of enhancing images by estimating reflectance and illumination in a retinex decomposition course. However, ambiguous details and unnatural color still challenge the performance of retinex variational models on underwater image enhancement. To overcome these limitations, we propose a hyper-laplacian reflectance priors inspired retinex variational model to enhance underwater images. Specifically, the hyper-laplacian reflectance priors are established with the l1/2 -norm penalty on first-order and second-order gradients of the reflectance. Such priors exploit sparsity-promoting and complete-comprehensive reflectance that is used to enhance both salient structures and fine-scale details and recover the naturalness of authentic colors. Besides, the l2 norm is found to be suitable for accurately estimating the illumination. As a result, we turn a complex underwater image enhancement issue into simple subproblems that separately and simultaneously estimate the reflection and the illumination that are harnessed to enhance underwater images in a retinex variational model. We mathematically analyze and solve the optimal solution of each subproblem. In the optimization course, we develop an alternating minimization algorithm that is efficient on element-wise operations and independent of additional prior knowledge of underwater conditions. Extensive experiments demonstrate the superiority of the proposed method in both subjective results and objective assessments over existing methods. The code is available at: https://github.com/zhuangpeixian/HLRP.