  In this paper we propose a numerical scheme for the class of backward doubly
stochastic (BDSDEs) with possible path-dependent terminal values. We prove that
our scheme converge in the strong $L^2$-sense and derive its rate of
convergence. As an intermediate step we derive an $L^2$-type regularity of the
solution to such BDSDEs. Such a notion of regularity which can be though of as
the modulus of continuity of the paths in an $L^2$-sense, is new.
