In this paper, a mathematical equation is developed for the equilibrium scour depth considering an arbitrary shape of the scour hole around a pier under the action of collinear waves and current. A power-law current velocity profile is assumed for the purpose of the analysis. The equilibrium scour depth is obtained by equating the work done by the flowing fluid while interacting with the pier under the action of the collinear waves and the current and the work done by the total volume of the sediment particles removed from the scour hole, respectively. The equilibrium scour depths predicted by the model show good agreement with the experimental and numerical results available in the literature.