This paper presents a finite element method for the analysis of linear water wave problems using the mesh optimization technique. The numerical model is based on the mild-slope equation. The hybrid element method is employed for the numerical treatment of the open boundary. The key feature of this method is that the approximation error based on the finite element discretization is estimated and the finite element mesh is redivided to minimize the total amount of the error. This follows that the accuracy of the numerical solutions is improved automatically. The numerical solutions obtained are compared with analytical solutions. The present method is shown to be an useful and effective method for the analysis of linear water wave problems.