Provided is a method for producing biodiesel fuel having an excellent oxidative stability and fluidity at low temperature, wherein the method provides selective hydrogenation of a poly-unsaturated fatty acid alkyl ester to the mono-unsaturated fatty acid alkyl ester while inhibiting the formation of the trans-isomer, and a biodiesel fuel composition. In the method for producing biodiesel fuel, a fatty acid alkyl ester prepared from fat and/or waste edible oil by transesterification reaction, and/or (2) a fatty acid alkyl ester treated by esterification reaction of a fatty acid is hydrogenated in the presence of a hydrogenation catalyst containing at least one of noble metals selected from those of Groups 8-10 in the periodic table under low hydrogen pressure.