Abstract: A space-time least-squares finite-element method is developed to solve the shollow water equation (SWE) which models the nonlinear long waves propagation. We use a regular propagating long wave in a constant slope bottom channel to verify accuracy of the model. Computed results agreed well with the exact solution. We then model a regular propagating long wave in a stepped bottom channel to demonstrate the bathymetry effects on wave deformations. Computed results show salient features of wave evolution, such as shoaling, wave reflection and decomposition. Spectrum analysis shows when the height of the step increases, the nonlinearity becomes significant, and high harmonics are generated.