The invention discloses a special clamp for abrasive flow polishing of a narrow flow passage closed impeller flow passage. The special clamp comprises an upper mold, a lower mold, a floating lock and a gasket support plate, wherein the upper mold and the lower mold form a cylindrical cavity; the inner diameter of the cylindrical cavity is greater than the diameter of the impellers; the gasket support plate is a round disc having the diameter as the same as the diameter of the impellers; the floating lock consists of an upper round disc and a lower round disc and a double-head stud and a bolt which are used for connecting the two round discs; the mounted floating lock can move between the gasket support plate and the lower mold; the impellers are arranged on the gasket support plate, and are fastened by the upper mold and the lower mold; and the upper mold and the lower mold are positioned through seam allowance, and are fixed by the bolts. The clamp for abrasive flow machining of the narrow plow passage closed impellers can be used for fixing the impellers and can guide abrasive materials to flow through the surface of the impeller flow passage, and keep a given pressure so as to grind and polish the internal part of the impeller flow passage, form a circular loop and realize reciprocating flow of the abrasive materials.