Abstract: Abstract The Total Variation Diminishing (TVD) schemes have been adapted to incompressible flow computations.Considering the characters of the computation in the incompressible flow,a new method is given that the TVD sheme is used with separating the continue equation from momentum equations.The continuum governing equations are discretized on a modified nonstaggered grid.In the momentum equations,the convective terms are discretized by a third order TVD scheme,and the others are done by central finite difference scheme.The pressures are solved by pressure substitiution.Furthermore,a pressure correction procedure and the Gauss-Seidel centrally symmetric iteration algorithm are used to enhance the convergence rate.As a result,the code containing those methods has been applied to computation of two typical flow problems:the channel flow problem and the lid driven cavity flow problem.A comparison of the present results with the literature data is also given in good agreement.It is shown that the TVD scheme is not only applicable to incomprssible flow computation,but also it yields higher accuracy than the non TVD scheme.