In this paper

we modify a class of low order accurate monotone schemes by using the Osher-Chakravarthy linear flux-modification schemes

and obtain a new high-order accurate different method for hyperbolic conservarion laws.For the Burgers equations and the Buckley-Leverett problem

mumerical results show that the presented method guarantees the stability and also performs well in keeping high order accuracy and avoiding the spurious oscillations.