HM Prison Leeds is a Category B men's prison, located at Gloucester Terrace in the Armley area of Leeds in West Yorkshire, England, which opened in 1847. Leeds Prison is operated by His Majesty's Prison Service, and is still known locally as Armley Gaol, the historical name of the prison.

Armley is a district in the west of Leeds, West Yorkshire, England. It starts less than 1 mile (1.6 km) from Leeds city centre. Like much of Leeds, Armley grew in the Industrial Revolution and had several mills, one of which now houses the Leeds Industrial Museum at Armley Mills. Armley is predominantly and historically a largely working class area of the city, still retains many smaller industrial businesses, and has many rows of back-to-back terraced houses.