To provide an abrasive allowing common use in coarse grinding and finish grinding even for a hard material such as hard steel or hard metal and applicable to precision grinding of a fine part and a small area part such as the groove or the corner part of the mold of a rib and a boss.

Alumina long fibers are bound together by matrix resin containing diamond abrasive grains with a diamond abrasive grain layer on the surface. For example, it is formed into a flat-plate shape having the thickness of 0.45 to 1.2 mm, with the diamond abrasive grain layer on at least either of the wide surfaces of both the front and rear sides thereof. A flat-shaped filament having a ratio of major axis to minor axis of 1.3 to 1.8 in its cross section is used as the alumina long-fiber.