HENRY CAVILL may have a supersize problem on his hands – his sexy GF isn’t happy about sharing the screen hunk with the world.

Henry, 30, began dating mixed martial arts fighter and actress Gina Carano last September, before his career skyrocketed with the release of the blockbuster “Man of Steel.” The flick raked in nearly $200 million worldwide in the first week after its release, making the British-born actor the toast of TinselTown.

“Henry is really lapping up the fame and glory,” a source told The ENQUIRER. “He knew he would be getting some notice for this, but his life is absolutely crazy right now.

“Gina is used to having Henry all to herself, and now she has to share him with the world. She really fears she’s going to be swept away by the rising tide of Henry’s career.”

Another source says that Gina, who found her own film fame with a butt-kicking role in “Fast & Furious 6” – has long wondered about her future with Henry. The pair began dating barely a month after Henry split from his British fiancée, professional horse-show jumper Ellen Whitaker.

“Gina was hoping Henry would stay grounded with the whirlwind around him, but she fears it’s going to his head,” the source revealed.

“All he’s talking about now is making a Superman sequel and winning the coveted starring role in the film version of ‘50 Shades of Grey.’”

 It’s a far cry from Henry’s childhood, when he was ridiculed for being overweight. And while Gina’s happy for her boyfriend’s success, the 31-year-old beauty is afraid of being left behind.

“Gina asked Henry point-blank: ‘Should I be looking for a way out of this relationship?’” the source added. “Henry told her she just needs to be patient.

“He said he spent more than 10 years as an actor when nobody knew who he was, and now he needs to ride this fame train and see where it goes.”