Reliable hydrodynamic modeling of rainfall-runoff processes in basins requires simulations with high resolution (or locally refined) meshes, which leads to a great increase in the computational costs in traditional GPU-accelerated (GPU: Graphics Processing Unit) hydrodynamic models. Here a GPU-accelerated and LTS-based (LTS: local time step) finite volume shallow water model is extended for rainfall-runoff simulations by coupling with the Green-Ampt model. The model performance is demonstrated by simulating four experimental and one field rainfall-runoff scenarios. A satisfactory agreement is obtained between simulation results and the available measured data for four experimental scenarios, indicating that the model can well simulate rainfall-runoff processes. When applied to the Hexi basin of Zhejiang Province, China, the model also captures the main patterns of rainfall-induced flooding, though model parameters cannot be well-specified. Inter-comparisons of the computational efficiency indicate that, implementing the LTS method brings considerable additional improvements over the GPU-acceleration, for simulations with uniform or nonuniform meshes. Specifically, the maximum speed-up ratio can be as high as over 10x for the present simulations.