Abstract: Approximate dispersion relation (ADR) may represent modified wave numbers of nonlinear schemes, and a numerical procedure is proposed to compute the ADR. The ADRs of the fifthorder nonlinear WENO5 and WCNS-E-5 finite difference schemes are compared with each other to show their spectral property. The results indicate that the dispersion error of the WCNS-E-5 is smaller than that of the WENO5, and the dissipation error of the WCNS-E-5 is also smaller than that of the WENO5. The whole spectral property of the WCNS-E-5 is better than that of the WENO5.