A higher-order flux-limited finite-difference scheme has been implemented into a compositional simulator to discretize the convection terms of the component conservation equations and the relative permeability terms of the phase fluxes. Harten＇s total variation diminishing criteria are imposed directly to the finite-difference equations and the bounds of the flux limiters which are suitable for larger Courant numbers and nonuniform grid systems are obtained. A time-correction technique is applied to increase the time accuracy and improve the stability condition. The scheme has been tested for miscible and immiscible flow problems in one and two dimensions, and the results were compared with those using a third-order method without flux limiting and some available analytical solutions. It has been shown that the scheme effectively reduces numerical dispersion and results in superior resolution of concentration and saturation fronts compared to conventional schemes. The stability conditions are also improved by using a time-correction technique. The results of the scheme are in good agreement with the analytical solutions. These improvements were achieved with negligible increase in computational effort. The scheme can also be applied to simulation problems with nonuniform gridblock sizes.