In this paper, we present an innovative finite volume surface-subsurface integrated flow model on nonorthogonal grids. The shallow water equation with diffusion wave approximation is used to formulate the surface flow system, while the Richards’ equation is used to formulate the saturated- unsaturated subsurface flow system. These two flow systems are discretized using a finite volume method and are then coupled by enforcing the continuity of pressure and flux at the surface-subsurface interface, which does not require unphysical parameters such as the interface permeability and thickness. The numerical instability caused by enforcing the continuity of pressure and flux at the interface is resolved using a cell-centered finite volume discretization. The coupled systems are solved simultaneously by the Newton iterative method. A battery of benchmark analyses and laboratory experiments verify the proposed model’s superior performance relative to existing models. Two numerical experiments over irregular terrain show that the nonorthogonal grids and diffusive wave approximation used in the proposed model accurately represent the interaction between surface and subsurface flows for irregular topographies. In particular, they capture the significant topographical effects on runoff discharges, especially where gentle slopes are involved.