The invention relates to a sectional type diesel particulate trapper using automatically regenerative metal foam filter elements. The trapping filter elements comprise cylindrical blocks which have different hole diameters and are pressed from through hole FeCrAl foam alloy; and the hole diameters of the filter elements are gradually reduced along the exhaust flow direction according to different sizes of particulate diameters of particulates discharged by a diesel engine. Therefore, the invention realizes the graded filter and the trap, improves the filter effect, reduces the trapper jam, slows the aging speed of the filter elements, improves the service life of the filter elements and has the function of noise elimination. The invention adopts a rare earth oxidation catalyst doped with a small amount of noble metal, HC and CO catalytically combust on the surfaces of the filter elements under the action of the catalyst when exhaust passes, heat released in the combustion combusts particulates, therefore, the automatic regeneration of the trapper is realized. The invention has the advantages of favorable filter effect, low cost, combined functions of multicomponent catalysis and noise elimination and easy adjustment according to engine power and emission regulations, thereby being well applied to diesel exhaust post-treatment.