In this paper, by choosing an ansatz consistent with the asymptotic forms of the correlation and response function, the self-consistent mode-coupling theory is generalized to the analysis of the dynamic scaling of the nonlocal Sun-Guo-Grant equation and the values of the dynamic exponent depending on nonlocal parameter ρ are calculated numerically for the substrate dimension d=1, 2 dimensions，respectively. The results obtained are compared with that of dynamic renormalization-group theory and scaling analysis.