TVD is a kind of advanced numerical convection discretization scheme, which has good numerical stability and calculation accuracy. It can avoid the numerical oscillation and false diffusion, so it has the potential to be applied in the transient thermal-hydraulic analysis with wave characteristics. In this paper, a program was developed based on the TVD scheme and a one-dimensional problem is used as an example to validate the program with different cases. This paper proves the validity of TVD scheme.