Nearly a fifth of A-level entries from private school pupils were awarded an A* this year, according to new statistics.
And around half of fee-paying schools' exam entries were awarded at least an A, almost double the national figure.
A high proportion of the schools' A-level results will have been in traditional academic subjects like science, according to Barnaby Lenon, chairman of the Independent Schools Council (ISC), who added that they also have a strong record in modern languages.
The statistics - published by the ISC - show the results of 475 independent schools, taking a range of qualifications including A-levels, the International Baccalaureate (IB), BTECs, the extended project and the Cambridge Pre-U examination.
The Council's analysis of the results revealed that for A-levels, 19.2% of entries from ISC-educated pupils were awarded an A*, up from 18% last year.
Around 50.5% of entries gained an A or A*, down from 51.3% in 2013.
National figures for all students in England, Wales and Northern Ireland - published last week - showed that just over one in four (26%) of exams were awarded an A* or A grade, down 0.3 percentage points on last summer. The proportion of A* grades handed out rose to 8.2%, up 0.6 percentage points on 2013.
The ISC's new analysis also concludes that 2,333 pupils (7.1% of those at ISC schools) scored three or more A* grades.
Boys out performed girls at the highest grade, with 7.6% of young men at ISC schools achieving this standard compared to 6.5% of young women.
Mr Lenon said: "Independent schools can be very proud of their pupils' excellent exam results, with more than half of their A-levels being graded A* or A, nearly double the national figure.
"What is remarkable is the number of candidates achieving three or more A* grades, which has increased to 7.1% this year, up from 5.8% last year. This is an impressive rise.
"Furthermore, independent schools continue to be strong in modern languages and a high proportion of the independent schools' A-levels will have been in the traditional subjects such as maths, physics, chemistry, biology.
"Many top university departments offering these subjects are dependent on independent school pupils for the quality of applicants they seek."
He added that alongside A-levels, there has also been a rise in take-up of alternative qualifications such as the IB and the Pre-U.
A separate analysis suggests that the top private school this year for A-levels was Wycombe Abbey, a private girls' boarding school in Buckinghamshire, which had the highest combined A-level and AS-level Ucas points score per candidate for the seventh year running.
Sixth-formers at the school notched up a string of top grades between them, giving each student an average Ucas points score of 514. This is equivalent to almost four A* grades each.
North London Collegiate School, a girls' day school, scored the highest in terms of the IB, with an average Ucas points score per candidate of 652.