In the paper, we make a detailed study on generalized Crewther Relation (GCR) between Adler function ($D$) and Gross-Llewellyn Smith sum rules coefficient ($C^{\rm GLS}$) by using newly suggested single-scale approach of principle maximum conformality (PMC). The resultant GCR is scheme-independent, whose residual scale dependence due to unknown higher-order terms are highly suppressed. Thus pre...