A lattice Boltzmann method for solving the shallow water equations and the advection-dispersion equation is developed and implemented on graphics processing unit (GPU)-based architectures. The proposed LBM is implemented to an NVIDIA Computing Processors. GPU computing is performed using the Jacket GPU engine for MATLAB and ArrayFire. Mass transport with velocity-dependent dispersion in shallow water flow is simulated by combining the MRT-LBM model and the TRT-LBM model. This talk will demonstrate the GPU parallel performance for modeling mass transport phenomena in shallow water flows.