Peter Cox, former interim principal of Baverstock Academy, said the school had "no future in its current state" and "should close as quickly as possible".
The academy is set to close in August, despite a campaign to save it.
A final government decision over the fate of the school, in Druids Heath, is due this summer.
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Mr Cox was interim principal of the Academy when he sent the letter to schools minister Lord Nash in November.
He wrote: "The academy is broken."
"By closing Baverstock we can remove the many jaundiced, fatigued and inadequate staff and start again with a new vision and purpose," the letter adds.
Mr Cox has since become CEO of the LEAP Academy Trust, which runs the schools.
The future of the school was plunged into uncertainty in 2015 following financial difficulties.
Its closure was announced despite a campaign to save it and a four-week consultation was launched.
The Department for Education said a new sponsor had not been found for the school, which has been in special measures since 2014.
Nearly 2,400 people signed an online petition which called the school "a constant force of stability to the community".
Steve McCabe, Labour MP for Birmingham Selly Oak, has backed the campaign to keep the school open and previously said the government had treated the parents, pupils and community "with utter disregard".
The BBC has attempted to contact Mr Cox for comment.
The school has a new acting head teacher.
The head teacher of a troubled academy called for his own "broken" school to be closed in a letter to the government, it has emerged.