The invention discloses a rubber plug mounting device and a medicine mixer assembling machine with the same. The rubber plug mounting device comprises a rubber plug conveying mechanism and a rubber plug clamping mechanism. The rubber plug conveying mechanism is used for conveying rubber plugs. The rubber plug clamping mechanism is used for clamping the rubber plugs on the rubber plug conveying mechanism and placing the rubber plugs into medicine mixing cups. The rubber plug mounting device is controlled by a PLC, and a feeding system which is composed of oscillating disks and tracks is used for conveying the rubber plugs to a set position of equipment. Working efficiency is effectively improved, manpower resources are saved, and product assembling quality of the medicine mixer assembling machine can be guaranteed.