Abstract: A new parabola interpolation is constructed to obtain a better differencing scheme suitable for the arbitrary meshes.The new scheme is sensitive to flow direction and needs only the nearest neighbor nodes.Two cases were selected to test its performance on the non-orthogonal grids.Predicting results were compared with the results of other schemes and Peric's benchmark solution.In comparison with CDS,the new parabola interpolation demonstrates slightly more accuracy,faster convergence rate and less oscillation.