Abstract: Various aglogrithms of least-squares finite-element methods (LSFEM) for convection-diffusion equation (CDE) and shal-low-water equations (SWE) are formulated. The associated condition number of the resulting system of equations is sys-tematically compared. It is found that condition number of the resulting system of equations depends on the choice of vari-ables, interpolations, and size of element (∆x). In general, a better conditioned system is obtained by introducing auxiliary variable with low-order interpolation. The developed better conditioned shallow-water model is used to simulate wave propagation over a submerged bar and wave propagation past an elliptical hump. Computed results are compared with ex-periment data and other numerical approximation, and show good agreement.