The purpose of the present invention is to provide a method for producing a high quality biodiesel fuel having excellent oxidation stability and few low-temperature deposits. This purpose can be achieved by the following: hydrogenating a biodiesel fuel so as to selectively convert unsaturated fatty acid monoglycerides and then removing fatty acid monoglycerides through precipitation; or using an adsorbent to further remove fatty acid monoglycerides to a high degree from the biodiesel fuel produced using the method mentioned above.