The neutron-gamma-ray-coupled albedo Monte Carlo (AMC) method has been developed and implemented in MORSE-I. The energy- and angle-dependent differential albedo data, which include secondary gamma rays, are calculated for a slab layer with one-dimensional transport theory. Fundamental formulas for this method are described. The applicability to shielding design of fusion reactors is confirmed by analyzing the radiation streaming experiment conducted at the Fusion Neutronics Source facility, Japan Atomic Energy Research Institute. The AMC method has reproduced well the experimental data of radiation dose rates and spectra with an accuracy of ∼10%. It is shown that the AMC method is several times more efficient than the ordinary Monte Carlo calculation in obtaining data necessary for the design with expected accuracy.