A door-closing assembly is used on a frameless glass door and has a body, a drive device, a mounting bracket and a holding device. The body has a mounting panel and a casing. The casing has an outer end, a transverse hole and a longitudinal hole. The longitudinal hole is formed in the outer end of the casing and communicates with the transverse hole. The drive device is mounted in the body and has a stationary post, a drive plug, a threaded plug and a spring. The stationary post is mounted inside the transverse hole. The drive plug is slidably mounted in the longitudinal hole and presses against the stationary post. The threaded plug is screwed in the longitudinal hole. The spring is held between the drive plug and the threaded plug. The mounting bracket is holds the stationary post in place. The holding device is mounted around the body.