This is a study on application of a TVD-Mccormack scheme for the computation of one-dimensional dam-break flows. The TVD scheme not only has the ability to damp out oscillations, but also does not contain terms with adjustable parameters. Moreover, the TVD-McCormack scheme does not cause any additional difficulty when dealing with the source term of the equation and retains second-order accuracy in both space and time. In this study, by appropriately designing the limiter functions, the TVD property can be achieved, and numerical oscillations near a jump discontinuities can be eliminated or reduced. Also, this numerical scheme has less computational errors when the direction of the predictor-corrector step is in the same direction as the shock wane propagation.