This paper presents the computational methods for moving boundary problems in the surface water and overland flow problems. In the surface water domain, the moving boundary is modeled using a moving grid method. The mathematical formulation of the governing equations in the Arbitrary-Lagrangian-Eulerian (ALE) form and the numerical methods including different grid moving algorithms an introduced. In the overland domain, the moving boundary is simulated with a fixed grid method. The governing equations for overland flow are simplified to a diffusive wave equation. A special algorithm is employed to handle the wetting-drying process of the floodplain. A new approach that combines the moving and fixed grid method is reported in this paper, in which a typical surface water body in the river and estuary is divided into the main river channel and the submerged floodplain and modeled a two different domains with interaction through the interface.