  In this paper, we consider a reflected backward stochastic differential
equation driven by a $G$-Brownian motion ($G$-BSDE), with the generator growing
quadratically in the second unknown. We obtain the existence by the penalty
method, and a priori estimates which implies the uniqueness, for solutions of
the $G$-BSDE. Moreover, focusing our discussion at the Markovian setting, we
give a nonlinear Feynman-Kac formula for solutions of a fully nonlinear partial
differential equation.
