Abstract: The Godunov scheme with an exact Riemann solution is used to solve the shallow water equations, and the classical Riemann solution on dry flat bed is improved to be suitable to the moving boundary with non-flat bed. Based on the verification of a dam-break wave on dry bed, the mathematical model is applied to calculate the tidal bore on the flat alluvial plain of the Qiantang Estuary with the improved Riemann solution on dry bed to solve the moving boundary. Calculation results show that the method can well simulate the propagation of the tidal bore.