JAKE GYLLENHALL’s new GF has a terrible family secret —  her grandfather was the right hand man to the notorious Shah of Iran!

Yet, Jake’s new girlfriend is a gorgeous New York City grad student that he met on an Amtrak train!

The 31-year-old “End of Watch” star was spotted arm-in-arm with his new “mystery girl” while strolling through NYC’s East Village on Nov. 9 – and The ENQUIRER can reveal that the raven-haired beauty is 26-year-old Mahsa Jafarian.

From her exotic good looks to her upbringing, it appears that Mahsa has little in common with the string of celebrities Jake’s dated over the years, in­cluding Kirsten Dunst, Reese Witherspoon and, most recent­ly, Taylor Swift.

“Mahsa’s family is  Chris­tian, and they fled from Iran during the 1979 Islamic revolution when the Shah was overthrown,” a source told The ENQUIRER.

“Her grandfather was the Shah’s right-hand man, and he was executed during the revolt.

“It was a devastating time for Mahsa’s mother and fa­ther. They immediately fled to the United States fearing they would be next.”

Mahsa was born seven years later, in 1986, in Penn­sylvania. She graduated from Brown University last year and is now enrolled in an MBA program at a college in New York City.

According to the source, Jake approached Mahsa on the train two months ago. At first, she had no idea he was a movie star, and they struck up a conversation.

“He asked for her number and gave her a call just a few days later to ask how she did on an exam she’d told him about,” said the source.

The pair then went on a few casual dates, and they’re hitting it off so well that Jake asked Mahsa to spend Thanksgiving with him and his mom in New York.

“She’s really excited about that,” the source added. “He also took her to dinner recently with Jerry Seinfeld and his wife.

“Mahsa thinks Jake is intelli­gent, well-rounded and a perfect gentleman – and she’s completely smitten with him.”