A fastening device includes a tubular sleeve member adapted to be sleeved around a tube. The sleeve member defines a space for receiving the tube therein and a notch. The sleeve member further has first and second through holes aligned with the notch and a nut reception space defined in the first through hole. A fixing element includes a fixing nut disposed within the nut reception space, a fixing bolt extending through the through holes to fasten the fixing nut threadedly and a tightening-enforcing element disposed exterior of the nut reception space and mounted on the fixing bolt such that tightening of the fixing element relative to the fixing nut in a first section and further tightening of the tightening-enforcing element relative to the fixing bolt in a second section results in pressing of the sleeve member against the tube, thereby immobilizing the sleeve member and the tube relative to each other.