  In this paper we extend the results of the seminal work Barles and Souganidis
\cite{BS} to path dependent case. Based on the viscosity theory of path
dependent PDEs, developed by Ekren, Keller, Touzi and Zhang \cite{EKTZ} and
Ekren, Touzi and Zhang \cite{ETZ0, ETZ1, ETZ2}, we show that a monotone scheme
converges to the unique viscosity solution of the (fully nonlinear) parabolic
path dependent PDE. An example of such monotone scheme is proposed. Moreover,
in the case that the solution is smooth enough, we obtain the rate of
convergence of our scheme.
