With the school leaving age set to be raised to 18, when students sit qualifications such as A-levels, national exams at age 16 are no longer relevant, according to Dr Helen Wright, the new president of the Girls' Schools Association.
Dr Wright told the Press Association news agency that a shake-up of how secondary school pupils were assessed was needed.
"On one level we are raising the school leaving age to 18, why do we need to focus on the age of 16? Why shouldn't we be looking at children earlier or later? There are certain things they need to be able to do, to be at a certain level in English and maths.
"But why are we focusing on a very academic form of assessment at the age of 16 and then at 18. Shouldn't we be scrapping the one at 16 or diminishing its value or importance? Maybe making it an internal school check and also possibly from an early age looking at different routes according to different rates and practices."
Dr Wright suggested there needs to be more flexibility to allow students to take different options at different times. For example, she said, a student may not be interested in taking GCSE French at 14, but may be interested in a one-year course at age 17.
She said Education Secretary Michael Gove was "right" to say children should know about core subjects such as English, maths, science and humanities.
"The question is, is it absolutely necessary to have them as GCSEs?" she said.
Dr Wright later added: "I think GCSEs have run their course."
There is a "big jump" between what teenagers are required to know at GCSE and A-level, Dr Wright added, which is why many schools now sit GCSEs earlier anyway, to allow more time for higher study.
Dr Wright is headmistress of the private girls boarding school St Mary's, at Calne, Wiltshire,