A medicine dispensing apparatus fills a vial having a polygonal cross-sectional shape with medicines to dispense the medicines. The apparatus contains a stocker, a first vial transporting unit, a vial orienting unit, a labeling unit, a second vial transporting unit, a medicine filling unit, and a vial discharging window. The stocker stores the vial. The first vial transporting unit transports the vial from the stocker to the labeling unit. The vial orienting unit adjusts an orientation of the vial. The labeling unit labels the vial. The second vial transporting unit transports the vial from the labeling unit to the medicine filling unit. The medicine filling unit fills the vial with the medicines. The second vial transporting unit further transports the vial from the medicine filling unit to the vial discharging window, where the vial is discharged through the vial discharging window.