The Cockburn Multi Academy Trust has submitted an application to open a new free school in Leeds.
It would create a minimum of 900 places in the inner south area of the city.
If the bid is approved by the Department for Education, the school would open in September 2018.
David Gurney, Headteacher of Cockburn School in Beeston, said: “Opening this free school would be a major step towards ensuring that there are enough excellent secondary school places in south Leeds.”
There is no fixed location for where the school could be built.
The Trust said it would address the need for more secondary school places in the inner south area of Leeds.
It would be called the The Laurence Calvert Academy after a former Cockburn School pupil who was awarded the Victoria Cross for bravery in 1918.
The school would open 100 years after Sergeant Calvert received his award, which he was given after he rushed a German machine gun post.