The invention relates to a three-jaw necking machine synchronizing by a rack, which comprises a supporting seat, a telescopic arm, a first rotating arm, a second rotating arm, three jaws, a first gear set, a second gear set and an executing cylinder, wherein the telescopic arm can be connected to the supporting seat in an up-and-down moving way, and a rack with a guide post is arranged below the telescopic arm; the first rotating arm and the second rotating arm are respectively connected to the supporting seat rotatablely by a first pin shaft and a second pin shaft and are also positioned at both sides of the telescopic arm symmetrically; each jaw is respectively connected to the first rotating arm, the second rotating arm and the telescopic arm; the first gear set is connected to the first rotating arm, the second gear set is connected to the second rotating arm, and the first gear set and the second gear set are symmetrically engaged with the rack with the guide post respectively; and the first rotating arm and the second rotating arm rotate around the axes of the first pin shaft and the second pin shaft respectively under the action of the executing cylinder also by the engaging relationship of the first gear set, the second gear set and the rack with the guide post, the telescopic arm is in telescopic movement on the supporting seat, and the three jaws move simultaneously under the driving of the first rotating arm, the second rotating arm and the telescopic arm respectively so as to present the arrangement of necking of the jaws or opening of the jaws.