This work develops a grid based rainfall-runoff model (GRM), which is a physically based and spatially distributed model. Surface flow was analyzed using a kinematic wave model with the governing equations discretized using the finite volume method (FVM). This paper suggests a grid network flow analysis technique using variable rainfall intensity according to the flow directions to analyze one-dimensional flows between the grids. The model was evaluated by applying it to the Wuicheon watershed, a tributary of the Nakdonggang (Riv.), in Korea. The results showed that the grid-based, one-dimensional kinematic wave model adopted the FVM and the grid network flow analysis technique well. The simulation results showed good agreement with the observed hydrographs and the initial soil saturation ratio was most sensitive to the modeling results.