Based on Fourier cosine expansion, two approximations of conditional expectations are studied, and the local errors for these approximations are analyzed. Using these approximations and the theta-time discretization, a new and efficient numerical scheme, which is based on least-squares regression, for forward-backward stochastic differential equations is proposed. Numerical experiments are done to test the availability and stability of this new scheme for Black-Scholes call and calls combination under an empirical expression about volatility. Some conclusions are given.