A centrifugal barrel polishing machine that polishes workpieces by rotating and revolving a barrel tank containing a mass including the workpieces and a polishing medium, comprising: a disc-like turret configured to turn about a revolution shaft; a plurality of barrel tanks each installed in the turret via a rotation shaft and configured to turn about the rotation shaft; a rotating mechanism configured to turn the turret and the barrel tanks; a tilting mechanism configured to tilt the revolution shaft of the turret with respect to a horizontal plane and to tilt each rotation shaft with respect to the horizontal plane;and rotation speed adjusting means for controlling a rotation speed of the rotation and revolution of the barrel tanks; characterized by further comprising a control unit configured to perform: a first acceleration step of adjusting the speed of the rotation and revolution of the barrel tanks using the rotation speed adjusting means such that the centrifugal force applied to the mass reaches a first centrifugal force, which is set as a centrifugal force immediately before the mass is separated from inner walls of each barrel tank with its own weight, within a first period of time; and a second acceleration step of adjusting the speed of the rotation and revolution of the barrel tanks using the rotation speed adjusting means such that the centrifugal force applied to the mass reaches a second centrifugal force, which is set as a centrifugal force for centrifugally bringing the mass into contact with the inner walls of each barrel tank, within a second period of time after the first acceleration step. a disc-like turret configured to turn about a revolution shaft; a plurality of barrel tanks each installed in the turret via a rotation shaft and configured to turn about the rotation shaft; a rotating mechanism configured to turn the turret and the barrel tanks; a tilting mechanism configured to tilt the revolution shaft of the turret with respect to a horizontal plane and to tilt each rotation shaft with respect to the horizontal plane;and rotation speed adjusting means for controlling a rotation speed of the rotation and revolution of the barrel tanks; characterized by further comprising a control unit configured to perform: a first acceleration step of adjusting the speed of the rotation and revolution of the barrel tanks using the rotation speed adjusting means such that the centrifugal force applied to the mass reaches a first centrifugal force, which is set as a centrifugal force immediately before the mass is separated from inner walls of each barrel tank with its own weight, within a first period of time; and a second acceleration step of adjusting the speed of the rotation and revolution of the barrel tanks using the rotation speed adjusting means such that the centrifugal force applied to the mass reaches a second centrifugal force, which is set as a centrifugal force for centrifugally bringing the mass into contact with the inner walls of each barrel tank, within a second period of time after the first acceleration step. a first acceleration step of adjusting the speed of the rotation and revolution of the barrel tanks using the rotation speed adjusting means such that the centrifugal force applied to the mass reaches a first centrifugal force, which is set as a centrifugal force immediately before the mass is separated from inner walls of each barrel tank with its own weight, within a first period of time; and a second acceleration step of adjusting the speed of the rotation and revolution of the barrel tanks using the rotation speed adjusting means such that the centrifugal force applied to the mass reaches a second centrifugal force, which is set as a centrifugal force for centrifugally bringing the mass into contact with the inner walls of each barrel tank, within a second period of time after the first acceleration step.