Images captured underwater often suffer from haze, noise, and low contrast owing to the absorption and scattering of water and suspended particles, making it difficult for analysis and understanding. To overcome these limitations, combined with an underwater optical image formation model, a fast variational approach based on a Laplace operator prior term is proposed herein to simultaneously perform dehazing and denoising. Based on the underwater optical image formation model, the data and regular items of the unified variational model are designed, wherein the Laplacian operator prior term is adopted as the regular term. The prior estimation of the improved red channel and the underwater red channel are used to obtain the global background light and the transmission map, respectively. To further accelerate the whole progress, a fast alternating direction multiplier method (ADMM) is introduced to solve the energy function. Our proposed variational method based on the Laplace operator prior term is executed on a set of representative real underwater images, demonstrating that it can successfully remove haze, suppress noise, and improve contrast and visibility.