Nicole Barr, 12, from Essex, scored an impressive 162 in the test, two points higher than both Hawking and Einstein.
Her parents say they are both proud of the schoolgirl, who is from the traveling community.
Mother Dolly Buckland, 34, said Barr was an extremely conscientious child who dreams of becoming a doctor.
“She’s a hard, hard working child. She stays after school for homework club and never misses a day.
“From a young age she’s been picking out mistakes in books and magazines. She’s a happy, fun-loving girl who is always asking for extra homework.
“She’s determined to finish school and go to college and university to be a pediatrician.”
James Barr, Nicole’s father, who repairs driveways for a living, said her achievement has been shared around the traveling community with pride, adding it is proof that brilliance can come from any background.
“The story has been going around the gypsy community, particularly on Facebook where it keeps being shared.
“It’s nice for us to be in the news for something good for a change. This shows that it doesn’t matter where you come from, anyone can be academically brilliant,” he said.
The average adult IQ score is 100, and any score over 140 is considered genius level. Eminent scientists Hawking and Einstein both scored 160 points.
Nicole, who is in Year 7 at Burnt Mill Academy in Harlow said: “When I found out I got such a high score, it was so unexpected. I was shocked.
“I remember when I was in primary school and I was an angel in a school play, another girl who was playing the other angel didn’t turn up so I learnt her lines too.”
Her head teacher praised Barr’s achievements, saying she was an exemplary pupil.
“Nicole is a brilliant pupil. She works incredibly hard and has thrown herself into many different activities in her first year with us.
“For example she has been camping, entered writing competitions and taken part in a national maths challenge.
“She lives and breathes our unofficial motto of hard work pays.”