The 79-year-old had just alighted from the single decker bus on the A255 Ramsgate Road, in Broadstairs, when he apparently stumbled as it pulled away.
He was pronounced dead at the scene after witnesses reported seeing him trapped under the vehicle. Kent Police said he lived locally.
Anyone who saw the incident, which happened at about 20:30 BST on Friday, is asked to contact officers.
An elderly man has died after falling into the path of a bus in Kent.