  In this paper, we build the equivalence between rough differential equations
driven by the lifted $G$-Brownian motion and the corresponding Stratonovich
type SDE through the Wong-Zakai approximation. The quasi-surely convergence
rate of Wong-Zakai approximation to $G-$SDEs with mesh-size $\frac{1}{n}$ in
the $\alpha$-H\"older norm is estimated as $(\frac{1}{n})^{\frac12-}.$ As
corollary, we obtain the quasi-surely continuity of the above RDEs with respect
to uniform norm.
