Jason Momoa Was 'Too Broke to Fly Home' While Filming 'Game of Thrones' Momoa posted a throwback photo of himself traveling around Ireland in a van while filming the br first season of the show. Jason Momoa, via Instagram He portrayed Khal Drogo in the hit series between 2011 and 2012. He revealed he has so many wonderful br stories from that part of his life. Momoa said it's been "a long road" to success and it's the "simplest moments" that he cherishes the most. He promised to share some more "gold" throwback pictures.