  We design a class of numerical schemes for backward stochastic differential
equation driven by $G$-Brownian motion ($G$-BSDE), which is related to a fully
nonlinear PDE. Based on Peng's central limit theorem, we employ the CLT method
to approximate $G$-distributed. Rigorous stability and convergence analysis are
also carried out. It is shown that the $\theta$-scheme admits a half order
convergence rate in the general case. In particular, for the case of
$\theta_{1}\in[0,1]$ and $\theta_{2}=0$, the scheme can reach first-order in
the deterministic case. Several numerical tests are given to support our
theoretical results.
