A pulling tool for gripping a cable or cables, especially fragile cables such as fiber optic cables. The pulling tool can pull such fragile cables with or without fragile connectors coupled to their free ends. The pulling tool has a mesh sleeve with an open tail end for receiving the ends of the cables, and a closed lead end with a ring or pulling member coupled thereto. The sleeve is constructed of a plurality of thin, flexible strands tightly interwoven together to form a longitudinally compressible and laterally expandable tube. The strands are tightly interwoven to prevent the cables or connectors from protruding outwardly from the sleeve. The sleeve is also highly flexible to permit the sleeve to be folded or rolled up.