Darren Williams, 39, died on Friday at HMP Woodhill in Milton Keynes, the Prison Service confirmed.
HMP Woodhill prison has been recently criticised for "high levels of boredom" and rising levels of violence and self-harm.
Police attended after being called at 16:00 GMT.
The death was not believed to be suspicious.
A statement from the Prison Service said its thoughts were with Mr Williams' family and friends.
Thames Valley Police added that a file was being prepared for the coroner.
HMP Woodhill had the highest suicide rate of all prisons in England and Wales in the five years to 2017.
In a report published in September, the Independent Monitoring Board (IMB) blamed "high levels of boredom" for an increase in violence and self-harm at the prison, while staff shortage problems had "chronic" consequences.
However, the IMB said there had been no suicides between 12 December 2016 and 10 May 2018 in its latest report.
