  In this paper, we present a numerical scheme to solve the initial-boundary
value problem for backward stochastic partial differential equations of
parabolic type. Based on the Galerkin method, we approximate the original
equation by a family of backward stochastic differential equations (BSDEs, for
short), and then solve these BSDEs by the time discretization. Combining the
truncation with respect to the spatial variable and the backward Euler method
on time variable, we obtain the global $L^2$ error estimate.
