We generalize the algorithm for semi-linear parabolic PDEs in
Henry-Labord\`ere (2012) to the non-Markovian case for a class of Backward SDEs
(BSDEs). By simulating the branching process, the algorithm does not need any
backward regression. To prove that the numerical algorithm converges to the
solution of BSDEs, we use the notion of viscosity solution of path dependent
PDEs introduced by Ekren, Keller, Touzi and Zhang (2012) and extended in Ekren,
Touzi and Zhang (2013).Comment: 31 page