Abstract: A new monotonicity limiter algorithm is presented,particularly suited for unstructured grid applications,so as to constrain the interpolated values on either side of the interface by imposing a monotonicity coefficient on the gradient of each cell.The coefficient depends not only on the local gradient value but also on the gradient values of the surrounding cells,so that the solutions obtained be devoid of the oscillation.Numerical computations of the nozzle flows have been carried out.The results show that in conjuction with the limiter,the second order Godunov scheme produces good resolution of shock.