The 2 quakes, happened in the space of half an hour, measured up to magnitude 7.0.
The epicentre of the quake was in the Ionian Sea, 35km (22miles) southwest of the beautiful Greek island of Zakynthos, popular with European tourists.
It was 124km (77miles) southwest of Patras on the Greek mainland.
The US Geological Survey said the first quake was just 10km below the surface, meaning the effects would have been felt more strongly above ground.
Casualties and damage figures aren’t yet known, but fire brigade officials in the capital Athens said there were no initial reports of casualties.