  In the paper, we reanalyze the properties of Gross-Llewellyn Smith (GLS) sum
rule by using the $\mathcal{O}(\alpha_s^4)$-order QCD corrections with the help
of principle of maximum conformality (PMC). By using the PMC single-scale
approach, we obtain an accurate renormalization scale-and-scheme independent
pQCD contribution for GLS sum rule, e.g. $S^{\rm GLS}(Q_0^2=3{\rm GeV}^2)|_{\rm
PMC}=2.559^{+0.023}_{-0.024}$, where the error is squared average of those from
$\Delta\alpha_s(M_Z)$, the predicted $\mathcal{O}(\alpha_s^5)$-order terms
predicted by using the Pad\'{e} approximation approach. After applying the PMC,
a more convergent pQCD series has been obtained, and the contributions from the
unknown higher-order terms are highly suppressed. In combination with the
nonperturbative high-twist contribution, our final prediction of GLS sum rule
agrees well with the experimental data given by the CCFR collaboration.
