In the footage the man can be seen staggering towards the tram doors at Castle Square before pushing the button to try and open the door.
However, despite his efforts, the tram sets off leaving the man to stumble alongside the carriage.
As the tram carries on the man then loses his footing and falls into the tram tracks and underneath the moving tram.
Trams were held between Castle and Square and Cathedral as emergency services attended the incident to help the man.
The man was helped from the scene with trams delayed for 15 minutes as a result of the incident.
A spokesperson for Supertram said: "We were aware of this incident that occurred over the weekend. Safety is our absolute priority and we have already begun an investigation into the circumstances surrounding the incident.
“Although not shown in this footage, our own CCTV footage shows that the driver stopped the tram as soon as the person fell over - the man pictured was not injured and walked away from the stop.
"We'd like to take the opportunity to remind customers about the safe use of trams. Once the doors have closed and the tram is ready to depart, customers should not attempt to board.”