At present,the numerical solution of one-dimensional two-fluid model is only first order.Safety design of advanced reactor depends on higher-ordered numerical scheme and code.This work aims at the investigation of the second-ordered scheme for the one-dimensional two-fluid model,to apply the second scheme for improving one first-order test code TFIT to second ordered.Flux-limiter scheme is used for the convection term,the surface tension term is adopted to make the numerical solution stable.The classical water wave problem-water faucet problem is used as the benchmark to test the second-ordered scheme.The numerical solutions of second-ordered and first-ordered scheme are compared with analytical solutions,and the comparison shows that the second-ordered solutions tend to analytical solutions better,catch the void wave of the water faucet problem well,and keep to the same stability of first-ordered code.