Police in the city of Alexandroupolis said the train on the Alexandroupolis-Ormenio line runs parallel to the Greek-Turkish border a few kilometers (miles) to the east.
It hit two people walking on the tracks at 12:50 am Saturday, shortly after its departure from Alexandroupolis. Police said one was killed and the other seriously injured.
Migrants crossing into Greece from Turkey often use rail tracks to walk along at night.
The train driver reported the incident and was delayed. Only minutes after resuming its journey, at 2:20 am, the train fatally hit a third person.
The victims' identities or nationalities were not known.
