A circular knitted tubular structure manufactured at low cost with use of a circular knitting machine is highly adaptable to bending due to flexibility, having tube inner and outer surfaces so soft that no abnormal noise is produced, and hence useful as a sleeve covering and thereby protecting a cable, such as an electrical wire and an optical fiber cable. The circular knitted tubular structure is formed of a fabric tape formed of circular knitted fabric having front yarn forming loops and back yarn having a higher heat shrinkage ratio than the front yarn and formed into a scrolled shape by letting the back yarn undergo heat shrinkage to have an overlap portion circumferentially overlapping 1.3 to 2.5 times. Apparatus for manufacturing the circular knitted tubular structure includes a furnace and a shape-forming jig.