Surface gravity wave has long been an important topic in the study of hydrodynamics. Here, we consider a two-dimensional surface wave for an incompressible, inviscid fluid and pay special attention to its interaction with the topography at the bottom. We use a Green’s function approach coupled with an appropriate perturbation calculation to compare with previous works, which involve experimental study, numerical simulation, or very cumbersome theoretical calculations that usually do not directly tell what is going on in a physically intuitive manner. Our aim in this work is to give a physically more appealing approach that can complement the works done by previous researchers. We also apply our approach to definite problems for comparison.