In a strap-band type connecting device (1), a strap band (3) has an array of teeth (8), each of which forms a bridged brace (10) between the neighbouring slits (8a) to make a helical thread (9a) engage with the bridged brace (10) when a rod screw (9) is brought at the helical thread (9a) into engagement with the slits (8a) within a housing (4). The bridged brace (10) is curvedly deformed to provide a width-reduced groove (10a) in its lengthwise direction (P) so as to form a cross piece segment (11, 13), a geometrical moment of inertia of which increases along a circumferential direction (R) of the strap band (3) with a sufficient rigidity provided to resist against a bending force from the helical thread (9a) upon rotationally operating the rod screw (9).