Karina Oakley was asked to question numbers and complete challenges in several different categories, including verbal ability, memory, handling a pencil and numbers and shapes.
Some of the answers showed a "wonderful imagination", according to Prof Joan Freeman, the child psychologist who used the Stanford-Binet IQ intelligence test.
When asked, 'What do you use your eyes for?' Karina answered: 'You close them when you go to sleep' and then also said: 'You put your contact lenses in them'.
Karina, from Guildford, Surrey, has an IQ 60 points above the mean for the population.
Prof Freeman said a score of 160 was rare, but was not unheard of. The test goes up to 170.
Her mother, Charlotte Fraser, who previously worked in marketing, and her father, Nick, a computer programmer, said their daughter had a very good memory.
Her mother said: "Quite a lot of people had said to me that Karina is quite smart, quite bright, quite clear with her speech and quick to pick things up.
"So I looked Prof Freeman up on the internet, and gave her a call to see if she would see her and get her tested. It was just a bit of fun really."
She added: "She seems to be quite aware of her surroundings, what's going on around her, she is very observant, she talks all the time, asks questions all the time.
"The nature verses nurture argument is a very interesting one.
"I have stayed at home with her for almost three years, I have always talked to her a lot, always tried to answer her questions, we do a lot of things, we go to the park and we are part of various groups. That must make a difference.
"I do not know whether it is that, combined with something that she was born with."
After the test, the professor concluded: "Karina is a lovely, responsive and friendly little girl. She is more than very bright and capable, she is gifted."She added: "Karina enjoyed the test. The pleasure she took in the mental challenge in itself I have found to be a sign of intelligence."Another two-year-old girl, Elise Tan-Roberts, from Edmonton, north London, was recently found to have an IQ of 156. She can count to 10 in English and Spanish and recite the phonetic alphabet. She could also name 35 capital cities.source