A vehicular vibration damping control apparatus calculates a correction torque to suppress vehicle body sprung vibration. In outputting a correction torque command to a driving/braking torque producing device, the control apparatus outputs a hunting time correction torque command smaller than a normal time correction toque command when a state in which amplitude of the correction torque is greater than or equal to a predetermined amplitude continues for a predetermined time length, and thereafter to return an output of the correction torque command from the hunting time correction torque command to the normal time correction torque command if a state in which the amplitude of the correction torque is smaller than or equal to the predetermined amplitude continues for a first predetermined time length. The frequency of performing the vibration damping control is increased by suppressing occurrence of hunting at the time of return to the normal vibration damping control.