A quick, economical and environmentally friendly, “green”, process for the continuous purification of biodiesel (fatty acid alkyl esters (FAAE)) is described using a powdered, granulated or extruded adsorbent. The adsorbent is contained in a column system and is regenerated for reuse multiple times. The process employs an adsorbent such as, but not limited to, carbon, silica, clay, zeolite or a metal silicate contained in a column to remove the impurities from fatty acid alkyl esters (FAAE) or crude biodiesel in a continuous process. The process utilizes the adsorbent column system for the purification of biodiesel, rather than water or filtration, to remove soaps and other impurities entrained in a crude biodiesel. The crude biodiesel is contacted with an adsorbent packed into a column, or multiple columns in series, for a sufficient amount of time to remove impurities such as, but not limited to, soaps, metals, free glycerin, sterol glucosides and many of the other impurities that reduce the stability of biodiesel. The resulting finished biodiesel exiting the column(s) is ready for the methanol recovery process. Once the adsorbent no longer removes the desired amount of impurities, it is regenerated for reuse. The solvent used for the regeneration process is reclaimed and reused by recycling it back to the transesterification reaction.