The Department of Education (DE) has made the move in order to cope with an expected increase in year eight pupil numbers in some areas, BBC wrote.
Most of the places are for schools in the Belfast, North Down and Ards areas.
However, Bangor Grammar School principal, Elizabeth Huddleson, told BBC News NI she was ‘deeply disappointed’ that it had been given no extra places.
In all, 413 additional places are being provided in 20 schools this September.
The DE sets the maximum number of pupils a school can admit every year.
Around half of post-primary schools in Northern Ireland are regularly oversubscribed which means they receive more applications from pupils than they have available places.
In 2017-18, the problem was particularly acute in Bangor and North Down.
That led some schools in the area to be given extra places for Year Eight pupils in 2018.
The department has now taken the decision to announce additional places in 20 schools, while the post-primary application process is still ongoing.
Bangor Academy, Strangford Integrated College and Hazelwood Integrated College are to get 40 extra places each.
Regent House Grammar School and Lisnagarvey High School will get 30 extra places, while Ashfield Boys' High School, Belfast Model School for Girls, Aquinas Grammar School, Lagan College, St. Pius X College in Magherafelt and St. Patrick's College in Dungannon are to get 20 additional places.
Priory Integrated College in Holywood is to get 23 more places, Ashfield Girls' High School 17 extra places and St. Columbanus' College in Bangor and St. Patrick's Academy in Dungannon 15 additional places each.
Dromore High School is to get 12 more Year Eight places, Strathearn School and Glastry College 10 each, Antrim Grammar School eight and Nendrum College three.
The DE said they had provided additional places at schools where the pressure on numbers was greatest.
"In 2019, it is estimated that the number of children transferring will be well over 2,500 higher than the number that transferred four years ago," a spokesperson said.
"This proactive move is intended to ensure the transfer procedure can successfully conclude while minimizing the number of children who are unplaced at the end of the procedure.”
Huddleson said that she was ‘saddened and deeply disappointed’ that Bangor Grammar had received no extra places despite offering to admit 40 additional pupils this year.
"This offer was to prevent a repeat of the pressure for places that was well publicized last year and to do the very best for our local community by way of affording more boys the opportunity to attend the local school of their choice," she said.
"It would seem that a number of boys in our area will now be deprived the opportunity of a local Bangor-based school option in favor of options which will involve travel and education outside their local area.
"Furthermore, it restricts the options for boys and parents seeking a grammar school place as most of the additional places have been allocated to nonselective schools.
"We are concerned that, at a time when there are more boys going through the system, the department's approach has unfairly disadvantaged boys by reducing the local grammar school options for academically inclined boys."
Primary seven pupils will find out what post-primary school they will transfer to on June 1, 2019.
Post-primary schools will still be able to apply for a temporary variation in enrolment numbers from the DE if they want to admit more pupils than their maximum intake this year.